Abstract
We compute the algebraic hull of the Kontsevich–Zorich cocycle over any $ \mathrm {GL}^+_2(\mathbb {R}) $ invariant subvariety of the Hodge bundle, and derive from this finiteness results on such subvarieties.
-
[SGA3] Schémas en groupes (SGA 3). Tome I. Propriétés générales des schémas en groupes, Gille, P. and Polo, P., Eds., Société Mathématique de France, Paris, 2011, vol. 7.
@book {SGA3, TITLE = {Schémas en groupes ({SGA} 3). {T}ome {I}. {P}ropriétés générales des schémas en groupes},
SERIES = {Documents Mathématiques (Paris) [Mathematical Documents(Paris)]},
VOLUME = {7},
EDITOR = {Gille, Philippe and Polo, Patrick},
NOTE = {Séminaire de Géométrie Algébrique du Bois Marie 1962--64. [Algebraic Geometry Seminar of Bois Marie 1962--64]; a seminar directed by M. Demazure and A. Grothendieck with the collaboration of M. Artin, J.-E. Bertin, P. Gabriel, M. Raynaud and J-P. Serre; revised and annotated edition of the 1970 French original},
PUBLISHER = {Société Mathématique de France, Paris},
YEAR = {2011},
PAGES = {xxviii+610},
ISBN = {978-2-85629-323-2},
MRCLASS = {14L15},
MRNUMBER = {2867621},
ZBLNUMBER = {1241.14003},
} -
[AEM]
A. Avila, A. Eskin, and M. Möller, "Symplectic and isometric ${ SL}(2,\Bbb R)$-invariant subbundles of the Hodge bundle," J. Reine Angew. Math., vol. 732, pp. 1-20, 2017.
@ARTICLE{AEM,
author = {Avila, Artur and Eskin, Alex and Möller, Martin},
title = {Symplectic and isometric {${\rm SL}(2,\Bbb R)$}-invariant subbundles of the {H}odge bundle},
journal = {J. Reine Angew. Math.},
fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
volume = {732},
year = {2017},
pages = {1--20},
issn = {0075-4102},
mrclass = {37C85 (32G15)},
mrnumber = {3717086},
doi = {10.1515/crelle-2014-0142},
url = {https://doi.org/10.1515/crelle-2014-0142},
zblnumber = {06801922},
} -
[ANW]
D. Aulicino, D. Nguyen, and A. Wright, "Classification of higher rank orbit closures in $\mathcal H^{{odd}}(4)$," J. Eur. Math. Soc. (JEMS), vol. 18, iss. 8, pp. 1855-1872, 2016.
@ARTICLE{ANW,
author = {Aulicino, David and Nguyen, Duc-Manh and Wright, Alex},
title = {Classification of higher rank orbit closures in {$\mathcal H^{\rm{odd}}(4)$}},
journal = {J. Eur. Math. Soc. (JEMS)},
fjournal = {Journal of the European Mathematical Society (JEMS)},
volume = {18},
year = {2016},
number = {8},
pages = {1855--1872},
issn = {1435-9855},
mrclass = {37D40 (32G15)},
mrnumber = {3518480},
mrreviewer = {Jayadev S. Athreya},
doi = {10.4171/JEMS/631},
url = {https://doi.org/10.4171/JEMS/631},
zblnumber = {1369.37044},
} -
[AW] P. Apisa and A. Wright, Marked points on translation surfaces.
@MISC{AW,
author = {Apisa, Paul and Wright, Alex},
title={Marked points on translation surfaces},
arxiv = {1708.03411},
} -
[BHM]
M. Bainbridge, P. Habegger, and M. Möller, "Teichmüller curves in genus three and just likely intersections in ${\bf G}^n_m\times {\bf G}^n_a$," Publ. Math. Inst. Hautes Études Sci., vol. 124, pp. 1-98, 2016.
@ARTICLE{BHM,
author = {Bainbridge, Matt and Habegger, Philipp and Möller, Martin},
title = {Teichmüller curves in genus three and just likely intersections in {${\bf G}^n_m\times {\bf G}^n_a$}},
journal = {Publ. Math. Inst. Hautes Études Sci.},
fjournal = {Publications Mathématiques. Institut de Hautes Études Scientifiques},
volume = {124},
year = {2016},
pages = {1--98},
issn = {0073-8301},
mrclass = {14H10 (32G15)},
mrnumber = {3578914},
mrreviewer = {Thomas A. Schmidt},
doi = {10.1007/s10240-016-0084-6},
url = {https://doi.org/10.1007/s10240-016-0084-6},
zblnumber = {1357.14038},
} -
[BM]
M. Bainbridge and M. Möller, "The Deligne-Mumford compactification of the real multiplication locus and Teichmüller curves in genus 3," Acta Math., vol. 208, iss. 1, pp. 1-92, 2012.
@ARTICLE{BM,
author = {Bainbridge, Matt and Möller, Martin},
title = {The {D}eligne-{M}umford compactification of the real multiplication locus and {T}eichmüller curves in genus 3},
journal = {Acta Math.},
fjournal = {Acta Mathematica},
volume = {208},
year = {2012},
number = {1},
pages = {1--92},
issn = {0001-5962},
mrclass = {14G35 (14Dxx 14Hxx)},
mrnumber = {2910796},
doi = {10.1007/s11511-012-0074-6},
url = {https://doi.org/10.1007/s11511-012-0074-6},
zblnumber = {1250.14014},
} -
[Ca]
K. Calta, "Veech surfaces and complete periodicity in genus two," J. Amer. Math. Soc., vol. 17, iss. 4, pp. 871-908, 2004.
@ARTICLE{Ca,
author = {Calta, Kariane},
title = {Veech surfaces and complete periodicity in genus two},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {17},
year = {2004},
number = {4},
pages = {871--908},
issn = {0894-0347},
mrclass = {37D40 (30F60 32G15 37E05 37E15)},
mrnumber = {2083470},
mrreviewer = {Christopher M. Judge},
doi = {10.1090/S0894-0347-04-00461-8},
url = {https://doi.org/10.1090/S0894-0347-04-00461-8},
zblnumber = {1073.37032},
} -
[EM]
A. Eskin and M. Mirzakhani, "Invariant and stationary measures for the action on moduli space," Publ. Math. Inst. Hautes Études Sci., p. 230, 2018.
@article{EM,
author = {Eskin, Alex and Mirzakhani, Maryam},
TITLE={Invariant and stationary measures for the action on moduli space},
year={2018},
month={Apr},
day = {17},
journal = {Publ. {M}ath. {I}nst. {H}autes \'{E}tudes {S}ci.},
fjournal = {Publications mathématiques. Institut de {H}autes \'{E}tudes de lÕIH\Õ{E}S},
issn = {1618-1913},
doi = {10.1007/s10240-018-0099-2},
url = {https://doi.org/10.1007/s10240-018-0099-2},
note = {published online 17 April 2018},
pages = {230 pp.},
} -
[EMM]
A. Eskin, M. Mirzakhani, and A. Mohammadi, "Isolation, equidistribution, and orbit closures for the ${ SL}(2,\Bbb R)$ action on moduli space," Ann. of Math. (2), vol. 182, iss. 2, pp. 673-721, 2015.
@ARTICLE{EMM,
author = {Eskin, Alex and Mirzakhani, Maryam and Mohammadi, Amir},
title = {Isolation, equidistribution, and orbit closures for the {${\rm SL}(2,\Bbb R)$} action on moduli space},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {182},
year = {2015},
number = {2},
pages = {673--721},
issn = {0003-486X},
mrclass = {58D27 (22F10 32G15 37C85 37D40 60B15)},
mrnumber = {3418528},
mrreviewer = {Boris Hasselblatt},
doi = {10.4007/annals.2015.182.2.7},
url = {https://doi.org/10.4007/annals.2015.182.2.7},
zblnumber = {1357.37040},
} -
[EMMW] A. Eskin, C. McMullen, R. Mukamel, and A. Wright, Billiards, quadrilaterals and moduli spaces.
@MISC{EMMW,
author = {Eskin, Alex and McMullen, Curtis and Mukamel, Ronen and Wright, Alex},
title = {Billiards, quadrilaterals and moduli spaces},
note = {preprint},
zblnumber = {},
} -
[sfilip_ssimple]
S. Filip, "Semisimplicity and rigidity of the Kontsevich-Zorich cocycle," Invent. Math., vol. 205, iss. 3, pp. 617-670, 2016.
@ARTICLE{sfilip_ssimple,
author = {Filip, Simion},
title = {Semisimplicity and rigidity of the {K}ontsevich-{Z}orich cocycle},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {205},
year = {2016},
number = {3},
pages = {617--670},
issn = {0020-9910},
mrclass = {32G20 (14D07 30F60 37D40)},
mrnumber = {3539923},
mrreviewer = {Christian Schnell},
doi = {10.1007/s00222-015-0643-3},
url = {https://doi.org/10.1007/s00222-015-0643-3},
zblnumber = {1368.14013},
} -
[sfilip_zero]
S. Filip, "Zero Lyapunov exponents and monodromy of the Kontsevich-Zorich cocycle," Duke Math. J., vol. 166, iss. 4, pp. 657-706, 2017.
@ARTICLE{sfilip_zero,
author = {Filip, Simion},
title = {Zero {L}yapunov exponents and monodromy of the {K}ontsevich-{Z}orich cocycle},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {166},
year = {2017},
number = {4},
pages = {657--706},
issn = {0012-7094},
mrclass = {37D25 (14D07 32G15 37D40)},
mrnumber = {3619303},
mrreviewer = {Jayadev S. Athreya},
doi = {10.1215/00127094-3715806},
url = {https://doi.org/10.1215/00127094-3715806},
zblnumber = {1370.37066},
} -
[sfilip_algebraicity]
S. Filip, "Splitting mixed Hodge structures over affine invariant manifolds," Ann. of Math. (2), vol. 183, iss. 2, pp. 681-713, 2016.
@ARTICLE{sfilip_algebraicity,
author = {Filip, Simion},
title = {Splitting mixed {H}odge structures over affine invariant manifolds},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {183},
year = {2016},
number = {2},
pages = {681--713},
issn = {0003-486X},
mrclass = {32S35 (14H55 37A20)},
mrnumber = {3450485},
mrreviewer = {Jayadev S. Athreya},
doi = {10.4007/annals.2016.183.2.5},
url = {https://doi.org/10.4007/annals.2016.183.2.5},
zblnumber = {1342.14015},
} -
[Etale]
E. Freitag and R. Kiehl, Étale Cohomology and the Weil Conjecture, Springer-Verlag, Berlin, 1988, vol. 13.
@BOOK{Etale,
author = {Freitag, Eberhard and Kiehl, Reinhardt},
title = {Étale Cohomology and the {W}eil Conjecture},
series = {Ergeb. Math. Grenzgeb.},
volume = {13},
note = {translated from the German by Betty S. Waterhouse and William C. Waterhouse, with an historical introduction by J. A. Dieudonné},
publisher = {Springer-Verlag, Berlin},
year = {1988},
pages = {xviii+317},
isbn = {3-540-12175-7},
mrclass = {14F20 (11G25 14G13)},
mrnumber = {0926276},
mrreviewer = {James Milne},
doi = {10.1007/978-3-662-02541-3},
url = {https://doi.org/10.1007/978-3-662-02541-3},
zblnumber = {0643.14012},
} -
[Forni_Matheus_survey]
G. Forni and C. Matheus, "Introduction to Teichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards," J. Mod. Dyn., vol. 8, iss. 3-4, pp. 271-436, 2014.
@ARTICLE{Forni_Matheus_survey,
author = {Forni, Giovanni and Matheus, Carlos},
title = {Introduction to {T}eichmüller theory and its applications to dynamics of interval exchange transformations, flows on surfaces and billiards},
journal = {J. Mod. Dyn.},
fjournal = {Journal of Modern Dynamics},
volume = {8},
year = {2014},
number = {3-4},
pages = {271--436},
issn = {1930-5311},
mrclass = {37D40 (30F10 30F60 32G15 32G20)},
mrnumber = {3345837},
mrreviewer = {Jayadev S. Athreya},
doi = {10.3934/jmd.2014.8.271},
url = {https://doi.org/10.3934/jmd.2014.8.271},
zblnumber = {1377.37057},
} -
[FMZ_lyap]
G. Forni, C. Matheus, and A. Zorich, "Lyapunov spectrum of invariant subbundles of the Hodge bundle," Ergodic Theory Dynam. Systems, vol. 34, iss. 2, pp. 353-408, 2014.
@ARTICLE{FMZ_lyap,
author = {Forni, Giovanni and Matheus, Carlos and Zorich, Anton},
title = {Lyapunov spectrum of invariant subbundles of the {H}odge bundle},
journal = {Ergodic Theory Dynam. Systems},
fjournal = {Ergodic Theory and Dynamical Systems},
volume = {34},
year = {2014},
number = {2},
pages = {353--408},
issn = {0143-3857},
mrclass = {32G15 (14H10 58A14)},
mrnumber = {3233697},
mrreviewer = {Fei Yu},
doi = {10.1017/etds.2012.148},
url = {https://doi.org/10.1017/etds.2012.148},
zblnumber = {1290.37002},
} -
[FMZ_zero]
G. Forni, C. Matheus, and A. Zorich, "Zero Lyapunov exponents of the Hodge bundle," Comment. Math. Helv., vol. 89, iss. 2, pp. 489-535, 2014.
@ARTICLE{FMZ_zero,
author = {Forni, Giovanni and Matheus, Carlos and Zorich, Anton},
title = {Zero {L}yapunov exponents of the {H}odge bundle},
journal = {Comment. Math. Helv.},
fjournal = {Commentarii Mathematici Helvetici. A Journal of the Swiss Mathematical Society},
volume = {89},
year = {2014},
number = {2},
pages = {489--535},
issn = {0010-2571},
mrclass = {37D25 (32G15 37D40)},
mrnumber = {3225454},
doi = {10.4171/CMH/325},
url = {https://doi.org/10.4171/CMH/325},
zblnumber = {1316.32010},
} -
[Forni_deviations]
G. Forni, "Deviation of ergodic averages for area-preserving flows on surfaces of higher genus," Ann. of Math. (2), vol. 155, iss. 1, pp. 1-103, 2002.
@ARTICLE{Forni_deviations,
author = {Forni, Giovanni},
title = {Deviation of ergodic averages for area-preserving flows on surfaces of higher genus},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {155},
year = {2002},
number = {1},
pages = {1--103},
issn = {0003-486X},
mrclass = {37A25 (32G15 37C40 37D25 37D40 37E35 53D25)},
mrnumber = {1888794},
mrreviewer = {Howard Masur},
doi = {10.2307/3062150},
url = {https://doi.org/10.2307/3062150},
zblnumber = {1034.37003},
} -
[Ham] U. Hamenstaedt, Typical and atypical properties of periodic Teichmüller geodesics, 2014.
@MISC{Ham,
author = {Hamenstaedt, Ursula},
title = {Typical and atypical properties of periodic {T}eichmüller geodesics},
arxiv = {1409.5978},
year = {2014},
zblnumber = {},
} -
[Hum] J. E. Humphreys, Linear Algebraic Groups, Springer-Verlag, New York, 1975, vol. 21.
@BOOK{Hum,
author = {Humphreys, James E.},
title = {Linear Algebraic Groups},
note = {Grad. Texts in Math.},
volume = {21},
publisher = {Springer-Verlag, New York},
year = {1975},
pages = {xiv+247},
mrclass = {20GXX (14LXX)},
mrnumber = {0396773},
mrreviewer = {T. Ono},
zblnumber = {0325.20039},
} -
[LNW]
E. Lanneau, D. Nguyen, and A. Wright, "Finiteness of Teichmüller curves in non-arithmetic rank $1$ orbit closures," Amer. J. Math., vol. 139, iss. 6, pp. 1449-1463, 2017.
@ARTICLE{LNW,
author = {Lanneau, Erwan and Nguyen, Duc-Manh and Wright, Alex},
title = {Finiteness of {T}eichmüller curves in non-arithmetic rank $1$ orbit closures},
journal = {Amer. J. Math.},
fjournal = {American Journal of Mathematics},
volume = {139},
year = {2017},
number = {6},
pages = {1449--1463},
issn = {0002-9327},
mrclass = {37D40 (14H40 53A15)},
mrnumber = {3730926},
doi = {10.1353/ajm.2017.0036},
url = {https://doi.org/10.1353/ajm.2017.0036},
zblnumber = {1382.32011},
} -
[Mc]
C. T. McMullen, "Billiards and Teichmüller curves on Hilbert modular surfaces," J. Amer. Math. Soc., vol. 16, iss. 4, pp. 857-885, 2003.
@ARTICLE{Mc,
author = {McMullen, Curtis T.},
title = {Billiards and {T}eichmüller curves on {H}ilbert modular surfaces},
journal = {J. Amer. Math. Soc.},
fjournal = {Journal of the American Mathematical Society},
volume = {16},
year = {2003},
number = {4},
pages = {857--885},
issn = {0894-0347},
mrclass = {32G15 (37D50)},
mrnumber = {1992827},
mrreviewer = {Richard Kenyon},
doi = {10.1090/S0894-0347-03-00432-6},
url = {https://doi.org/10.1090/S0894-0347-03-00432-6},
zblnumber = {1030.32012},
} -
[McM:spin]
C. T. McMullen, "Teichmüller curves in genus two: Discriminant and spin," Math. Ann., vol. 333, iss. 1, pp. 87-130, 2005.
@ARTICLE{McM:spin,
author = {McMullen, Curtis T.},
title = {Teichmüller curves in genus two: {D}iscriminant and spin},
journal = {Math. Ann.},
fjournal = {Mathematische Annalen},
volume = {333},
year = {2005},
number = {1},
pages = {87--130},
issn = {0025-5831},
mrclass = {32G15 (30F10 37D50)},
mrnumber = {2169830},
mrreviewer = {Thomas A. Schmidt},
doi = {10.1007/s00208-005-0666-y},
url = {https://doi.org/10.1007/s00208-005-0666-y},
zblnumber = {1086.14024},
} -
[Mc7]
C. T. McMullen, "Teichmüller curves in genus two: The decagon and beyond," J. Reine Angew. Math., vol. 582, pp. 173-199, 2005.
@ARTICLE{Mc7,
author = {McMullen, Curtis T.},
title = {Teichmüller curves in genus two: {T}he decagon and beyond},
journal = {J. Reine Angew. Math.},
fjournal = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
volume = {582},
year = {2005},
pages = {173--199},
issn = {0075-4102},
mrclass = {32G15},
mrnumber = {2139715},
mrreviewer = {Thomas A. Schmidt},
doi = {10.1515/crll.2005.2005.582.173},
url = {https://doi.org/10.1515/crll.2005.2005.582.173},
zblnumber = {1073.32004},
} -
[Mc2] C. T. McMullen, "Prym varieties and Teichmüller curves," Duke Math. J., vol. 133, iss. 3, pp. 569-590, 2006.
@ARTICLE{Mc2,
author = {McMullen, Curtis T.},
title = {Prym varieties and {T}eichmüller curves},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {133},
year = {2006},
number = {3},
pages = {569--590},
issn = {0012-7094},
mrclass = {32G15 (14H40 37D50 57M50)},
mrnumber = {2228463},
mrreviewer = {Thomas A. Schmidt},
zblnumber = {1099.14018},
} -
[McMullen_classification]
C. T. McMullen, "Dynamics of ${ SL}_2(\Bbb R)$ over moduli space in genus two," Ann. of Math. (2), vol. 165, iss. 2, pp. 397-456, 2007.
@ARTICLE{McMullen_classification,
author = {McMullen, Curtis T.},
title = {Dynamics of {${\rm SL}_2(\Bbb R)$} over moduli space in genus two},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {165},
year = {2007},
number = {2},
pages = {397--456},
issn = {0003-486X},
mrclass = {32G15 (37C85 37F99)},
mrnumber = {2299738},
mrreviewer = {Serge L. Tabachnikov},
doi = {10.4007/annals.2007.165.397},
url = {https://doi.org/10.4007/annals.2007.165.397},
zblnumber = {1131.14027},
} -
[MMW]
C. T. McMullen, R. E. Mukamel, and A. Wright, "Cubic curves and totally geodesic subvarieties of moduli space," Ann. of Math. (2), vol. 185, iss. 3, pp. 957-990, 2017.
@ARTICLE{MMW,
author = {McMullen, Curtis T. and Mukamel, Ronen E. and Wright, Alex},
title = {Cubic curves and totally geodesic subvarieties of moduli space},
journal = {Ann. of Math. (2)},
fjournal = {Annals of Mathematics. Second Series},
volume = {185},
year = {2017},
number = {3},
pages = {957--990},
issn = {0003-486X},
mrclass = {32G15 (14H10)},
mrnumber = {3664815},
mrreviewer = {Christian Frederik Wei\ss },
doi = {10.4007/annals.2017.185.3.6},
url = {https://doi.org/10.4007/annals.2017.185.3.6},
zblnumber = {06731862},
} -
[M3]
M. Möller, "Finiteness results for Teichmüller curves," Ann. Inst. Fourier (Grenoble), vol. 58, iss. 1, pp. 63-83, 2008.
@ARTICLE{M3,
author = {Möller, Martin},
title = {Finiteness results for {T}eichmüller curves},
journal = {Ann. Inst. Fourier (Grenoble)},
fjournal = {Université de Grenoble. Annales de l'Institut Fourier},
volume = {58},
year = {2008},
number = {1},
pages = {63--83},
issn = {0373-0956},
mrclass = {14H10 (32G15 32G20)},
mrnumber = {2401216},
mrreviewer = {Pierre A. Lochak},
doi = {10.5802/aif.2344},
zblnumber = {1140.14010},
} -
[Masur_Tab]
H. Masur and S. Tabachnikov, "Rational billiards and flat structures," in Handbook of Dynamical Systems, Vol. 1A, North-Holland, Amsterdam, 2002, pp. 1015-1089.
@INCOLLECTION{Masur_Tab,
author = {Masur, Howard and Tabachnikov, Serge},
title = {Rational billiards and flat structures},
booktitle = {Handbook of Dynamical Systems, {V}ol. 1{A}},
pages = {1015--1089},
publisher = {North-Holland, Amsterdam},
year = {2002},
mrclass = {37-02 (28D05 30F60 37A25 37D50 37F99)},
mrnumber = {1928530},
mrreviewer = {Richard Kenyon},
doi = {10.1016/S1874-575X(02)80015-7},
url = {https://doi.org/10.1016/S1874-575X(02)80015-7},
zblnumber = {1057.37034},
} -
[MirWri]
M. Mirzakhani and A. Wright, "The boundary of an affine invariant submanifold," Invent. Math., vol. 209, iss. 3, pp. 927-984, 2017.
@ARTICLE{MirWri,
author = {Mirzakhani, Maryam and Wright, Alex},
title = {The boundary of an affine invariant submanifold},
journal = {Invent. Math.},
fjournal = {Inventiones Mathematicae},
volume = {209},
year = {2017},
number = {3},
pages = {927--984},
issn = {0020-9910},
mrclass = {37D40 (32G15 58A35)},
mrnumber = {3681397},
mrreviewer = {Jayadev S. Athreya},
doi = {10.1007/s00222-017-0722-8},
url = {https://doi.org/10.1007/s00222-017-0722-8},
zblnumber = {1378.37069},
} -
[MW]
C. Matheus and A. Wright, "Hodge-Teichmüller planes and finiteness results for Teichmüller curves," Duke Math. J., vol. 164, iss. 6, pp. 1041-1077, 2015.
@ARTICLE{MW,
author = {Matheus, Carlos and Wright, Alex},
title = {Hodge-{T}eichmüller planes and finiteness results for {T}eichmüller curves},
journal = {Duke Math. J.},
fjournal = {Duke Mathematical Journal},
volume = {164},
year = {2015},
number = {6},
pages = {1041--1077},
issn = {0012-7094},
mrclass = {37D40 (30F60 32G15)},
mrnumber = {3336840},
mrreviewer = {Jayadev S. Athreya},
doi = {10.1215/00127094-2885655},
url = {https://doi.org/10.1215/00127094-2885655},
zblnumber = {1345.37029},
} -
[Wtot] A. Wright, Totally geodesic submanifolds of Teichmüller space.
@MISC{Wtot,
author = {Wright, Alex},
title = {{T}otally geodesic submanifolds of {T}eichm{ü}ller space},
note = {forthcoming},
zblnumber = {},
} -
[AW_field]
A. Wright, "The field of definition of affine invariant submanifolds of the moduli space of abelian differentials," Geom. Topol., vol. 18, iss. 3, pp. 1323-1341, 2014.
@ARTICLE{AW_field,
author = {Wright, Alex},
title = {The field of definition of affine invariant submanifolds of the moduli space of abelian differentials},
journal = {Geom. Topol.},
fjournal = {Geometry \& Topology},
volume = {18},
year = {2014},
number = {3},
pages = {1323--1341},
issn = {1465-3060},
mrclass = {32G15 (30F60 37D40)},
mrnumber = {3254934},
mrreviewer = {Jayadev S. Athreya},
doi = {10.2140/gt.2014.18.1323},
url = {https://doi.org/10.2140/gt.2014.18.1323},
zblnumber = {1320.32019},
} -
[Wcyl]
A. Wright, "Cylinder deformations in orbit closures of translation surfaces," Geom. Topol., vol. 19, iss. 1, pp. 413-438, 2015.
@ARTICLE{Wcyl,
author = {Wright, Alex},
title = {Cylinder deformations in orbit closures of translation surfaces},
journal = {Geom. Topol.},
fjournal = {Geometry \& Topology},
volume = {19},
year = {2015},
number = {1},
pages = {413--438},
issn = {1465-3060},
mrclass = {32G15 (37D40)},
mrnumber = {3318755},
mrreviewer = {Jayadev S. Athreya},
doi = {10.2140/gt.2015.19.413},
url = {https://doi.org/10.2140/gt.2015.19.413},
zblnumber = {1318.32021},
} -
[Wsurvey]
A. Wright, "Translation surfaces and their orbit closures: an introduction for a broad audience," EMS Surv. Math. Sci., vol. 2, iss. 1, pp. 63-108, 2015.
@ARTICLE{Wsurvey,
author = {Wright, Alex},
title = {Translation surfaces and their orbit closures: an introduction for a broad audience},
journal = {EMS Surv. Math. Sci.},
fjournal = {EMS Surveys in Mathematical Sciences},
volume = {2},
year = {2015},
number = {1},
pages = {63--108},
issn = {2308-2151},
mrclass = {32G15 (30D05 30F30 30F60)},
mrnumber = {3354955},
mrreviewer = {Jayadev S. Athreya},
doi = {10.4171/EMSS/9},
url = {https://doi.org/10.4171/EMSS/9},
zblnumber = {1372.37090},
} -
[Zimmer_book]
R. J. Zimmer, Ergodic Theory and Semisimple Groups, Birkhäuser Verlag, Basel, 1984, vol. 81.
@BOOK{Zimmer_book,
author = {Zimmer, Robert J.},
title = {Ergodic Theory and Semisimple Groups},
series = {Monogr. Math.},
volume = {81},
publisher = {Birkhäuser Verlag, Basel},
year = {1984},
pages = {x+209},
isbn = {3-7643-3184-4},
mrclass = {22E40 (22D40 28D15)},
mrnumber = {0776417},
mrreviewer = {S. G. Dani},
doi = {10.1007/978-1-4684-9488-4},
url = {https://doi.org/10.1007/978-1-4684-9488-4},
zblnumber = {0571.58015},
} -
[Zorich_survey] A. Zorich, "Flat surfaces," in Frontiers in Number Theory, Physics, and Geometry. I, Springer, Berlin, 2006, pp. 437-583.
@INCOLLECTION{Zorich_survey,
author = {Zorich, Anton},
title = {Flat surfaces},
booktitle = {Frontiers in Number Theory, Physics, and Geometry. {I}},
pages = {437--583},
publisher = {Springer, Berlin},
year = {2006},
mrclass = {37D40 (30F30 32G15 37D50 57M50)},
mrnumber = {2261104},
mrreviewer = {Thomas A. Schmidt},
zblnumber = {1129.32012},
}