Abstract
In this paper we complete the proof of Căldăraru’s conjecture on the compatibility between the module structures on differential forms over poly-vector fields and on Hochschild homology over Hochschild cohomology. In fact we show that twisting with the square root of the Todd class gives an isomorphism of precalculi between these pairs of objects.
Our methods use formal geometry to globalize the local formality quasi-isomorphisms introduced by Kontsevich and Shoikhet. (The existence of the latter was conjectured by Tsygan.) We also rely on the fact — recently proved by the first two authors — that Shoikhet’s quasi-isomorphism is compatible with cap products after twisting with a Maurer-Cartan element.
-
[Bau]
H. J. Baues, "The double bar and cobar constructions," Compositio Math., vol. 43, iss. 3, pp. 331-341, 1981.@article {Bau, MRKEY = {0632433},
AUTHOR = {Baues, H. J.},
TITLE = {The double bar and cobar constructions},
JOURNAL = {Compositio Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {43},
YEAR = {1981},
NUMBER = {3},
PAGES = {331--341},
ISSN = {0010-437X},
CODEN = {CMPMAF},
MRCLASS = {55P35 (57T30)},
MRNUMBER = {0632433},
MRREVIEWER = {R. M. Vogt},
URL = {http://www.numdam.org/item?id=CM_1981__43_3_331_0},
ZBLNUMBER = {0478.57027},
} -
[Cal] D. Calaque, "Formality for Lie algebroids," Comm. Math. Phys., vol. 257, iss. 3, pp. 563-578, 2005.
@article {Cal, MRKEY = {2164943},
AUTHOR = {Calaque, Damien},
TITLE = {Formality for {L}ie algebroids},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {257},
YEAR = {2005},
NUMBER = {3},
PAGES = {563--578},
ISSN = {0010-3616},
CODEN = {CMPHAY},
MRCLASS = {53D55},
MRNUMBER = {2164943},
MRREVIEWER = {Dominique Manchon},
DOI = {10.1007/s00220-005-1350-5},
ZBLNUMBER = {1079.53138},
} -
[CDH] D. Calaque, V. Dolgushev, and G. Halbout, "Formality theorems for Hochschild chains in the Lie algebroid setting," J. Reine Angew. Math., vol. 612, pp. 81-127, 2007.
@article {CDH, MRKEY = {2364075},
AUTHOR = {Calaque, Damien and Dolgushev, Vasiliy and Halbout, Gilles},
TITLE = {Formality theorems for {H}ochschild chains in the {L}ie algebroid setting},
JOURNAL = {J. Reine Angew. Math.},
FJOURNAL = {Journal für die Reine und Angewandte Mathematik. [Crelle's Journal]},
VOLUME = {612},
YEAR = {2007},
PAGES = {81--127},
ISSN = {0075-4102},
CODEN = {JRMAA8},
MRCLASS = {53D55 (16E40 16E45 17B56)},
MRNUMBER = {2364075},
MRREVIEWER = {Beno\^ ıt Fresse},
DOI = {10.1515/CRELLE.2007.085},
ZBLNUMBER = {1141.53084},
} -
[CR] D. Calaque and C. A. Rossi, Lectures on Duflo Isomorphisms in Lie Algebra and Complex Geometry, European Mathematical Society (EMS), Zürich, 2011.
@book {CR, MRKEY = {2816610},
AUTHOR = {Calaque, Damien and Rossi, Carlo A.},
TITLE = {Lectures on {D}uflo Isomorphisms in {L}ie Algebra and Complex Geometry},
SERIES = {EMS Ser. Lect. Math.},
PUBLISHER = {European Mathematical Society (EMS), Zürich},
YEAR = {2011},
PAGES = {viii+106},
ISBN = {978-3-03719-096-8},
MRCLASS = {53Dxx (13Dxx 17Bxx)},
MRNUMBER = {2816610},
DOI = {10.4171/096},
ZBLNUMBER = {1220.53006},
} -
[CR1] D. Calaque and C. A. Rossi, "Shoikhet’s conjecture and Duflo isomorphism on (co)invariants," SIGMA Symmetry Integrability Geom. Methods Appl., vol. 4, p. 060, 2008.
@article {CR1, MRKEY = {2434938},
AUTHOR = {Calaque, Damien and Rossi, Carlo A.},
TITLE = {Shoikhet's conjecture and {D}uflo isomorphism on (co)invariants},
JOURNAL = {SIGMA Symmetry Integrability Geom. Methods Appl.},
FJOURNAL = {SIGMA. Symmetry, Integrability and Geometry. Methods and Applications},
VOLUME = {4},
YEAR = {2008},
PAGES = {Paper 060, 17},
ISSN = {1815-0659},
MRCLASS = {16E45 (16E40 17B55 81S10)},
MRNUMBER = {2434938},
MRREVIEWER = {Atabey Kaygun},
DOI = {10.3842/SIGMA.2008.060},
ZBLNUMBER = {1196.53044},
} -
[CR2] D. Calaque and C. A. Rossi, "Compatibility with cap-products in Tsygan’s formality and homological Duflo isomorphism," Lett. Math. Phys., vol. 95, iss. 2, pp. 135-209, 2011.
@article {CR2, MRKEY = {2764337},
AUTHOR = {Calaque, Damien and Rossi, Carlo A.},
TITLE = {Compatibility with cap-products in {T}sygan's formality and homological {D}uflo isomorphism},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics},
VOLUME = {95},
YEAR = {2011},
NUMBER = {2},
PAGES = {135--209},
ISSN = {0377-9017},
CODEN = {LMPHDY},
MRCLASS = {53D55 (16E40 16E45)},
MRNUMBER = {2764337},
MRREVIEWER = {Jeremy Lee Pecharich},
DOI = {10.1007/s11005-010-0451-z},
ZBLNUMBER = {1213.81142},
} -
[CVdB] D. Calaque and M. Van den Bergh, "Hochschild cohomology and Atiyah classes," Adv. Math., vol. 224, iss. 5, pp. 1839-1889, 2010.
@article {CVdB, MRKEY = {2646112},
AUTHOR = {Calaque, Damien and Van den Bergh, Michel},
TITLE = {Hochschild cohomology and {A}tiyah classes},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {224},
YEAR = {2010},
NUMBER = {5},
PAGES = {1839--1889},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {14F05 (14D23 14F43 18G55 53D55)},
MRNUMBER = {2646112},
MRREVIEWER = {Jeremy Lee Pecharich},
DOI = {10.1016/j.aim.2010.01.012},
ZBLNUMBER = {1197.14017},
} -
[CRVdB2] D. Calaque, C. A. Rossi, and M. van den Bergh, "Hochschild (co)homology for Lie algebroids," Int. Math. Res. Not., vol. 2010, iss. 21, pp. 4098-4136, 2010.
@article {CRVdB2, MRKEY = {2738352},
AUTHOR = {Calaque, Damien and Rossi, Carlo A. and van den Bergh, Michel},
TITLE = {Hochschild (co)homology for {L}ie algebroids},
JOURNAL = {Int. Math. Res. Not.},
FJOURNAL = {International Mathematics Research Notices. IMRN},
YEAR = {2010},
NUMBER = {21},
PAGES = {4098--4136},
ISSN = {1073-7928},
MRCLASS = {14F05 (16E40)},
MRNUMBER = {2738352},
MRREVIEWER = {Paolo Stellari},
DOI = {10.1093/imrn/rnq033},
VOLUME = {2010},
ZBLNUMBER = {1215.14006},
} -
[Cald] A. Cualduararu, "The Mukai pairing. II. The Hochschild-Kostant-Rosenberg isomorphism," Adv. Math., vol. 194, iss. 1, pp. 34-66, 2005.
@article {Cald, MRKEY = {2141853},
AUTHOR = {C{\u{a}}ld{\u{a}}raru, Andrei},
TITLE = {The {M}ukai pairing. {II}. {T}he {H}ochschild-{K}ostant-{R}osenberg isomorphism},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {194},
YEAR = {2005},
NUMBER = {1},
PAGES = {34--66},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {14F40 (19L10)},
MRNUMBER = {2141853},
MRREVIEWER = {David Ploog},
DOI = {10.1016/j.aim.2004.05.012},
ZBLNUMBER = {1098.14011},
} -
[Dol] V. Dolgushev, "A formality theorem for Hochschild chains," Adv. Math., vol. 200, iss. 1, pp. 51-101, 2006.
@article {Dol, MRKEY = {2199629},
AUTHOR = {Dolgushev, Vasiliy},
TITLE = {A formality theorem for {H}ochschild chains},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {200},
YEAR = {2006},
NUMBER = {1},
PAGES = {51--101},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {16E45 (16E05 53D17 53D55)},
MRNUMBER = {2199629},
MRREVIEWER = {Pasha Zusmanovich},
DOI = {10.1016/j.aim.2004.10.017},
ZBLNUMBER = {1106.53054},
} -
[DTT1] V. Dolgushev, D. Tamarkin, and B. Tsygan, "The homotopy Gerstenhaber algebra of Hochschild cochains of a regular algebra is formal," J. Noncommut. Geom., vol. 1, iss. 1, pp. 1-25, 2007.
@article {DTT1, MRKEY = {2294189},
AUTHOR = {Dolgushev, Vasiliy and Tamarkin, Dmitry and Tsygan, Boris},
TITLE = {The homotopy {G}erstenhaber algebra of {H}ochschild cochains of a regular algebra is formal},
JOURNAL = {J. Noncommut. Geom.},
FJOURNAL = {Journal of Noncommutative Geometry},
VOLUME = {1},
YEAR = {2007},
NUMBER = {1},
PAGES = {1--25},
ISSN = {1661-6952},
MRCLASS = {18D50 (16E40 16E45 53D55)},
MRNUMBER = {2294189},
MRREVIEWER = {Beno\^ ıt Fresse},
DOI = {10.4171/JNCG/1},
ZBLNUMBER = {1151.53076},
ZBLNUMBER = {1144.18007},
} -
[DTT2] V. Dolgushev, D. Tamarkin, and B. Tsygan, Formality of the homotopy calculus algebra of Hochschild (co)chains, 2008.
@misc{DTT2,
author = {Dolgushev, Vasiliy and Tamarkin, Dmitry and Tsygan, Boris},
TITLE = {Formality of the homotopy calculus algebra of {H}ochschild (co)chains},
ARXIV={0807.5117},
YEAR={2008},
} -
[GV] A. A. Voronov and M. Gerstenkhaber, "Higher-order operations on the Hochschild complex," Funktsional. Anal. i Prilozhen., vol. 29, iss. 1, pp. 1-6, 96, 1995.
@article {GV, MRKEY = {1328534},
AUTHOR = {Voronov, A. A. and Gerstenkhaber, M.},
TITLE = {Higher-order operations on the {H}ochschild complex},
JOURNAL = {Funktsional. Anal. i Prilozhen.},
FJOURNAL = {Rossiĭskaya Akademiya Nauk. Funktsional\cprime nyĭAnaliz i ego Prilozheniya},
VOLUME = {29},
YEAR = {1995},
NUMBER = {1},
PAGES = {1--6, 96},
ISSN = {0374-1990},
MRCLASS = {18G60 (16E40 19D55 55S20)},
MRNUMBER = {1328534},
MRREVIEWER = {J. Stasheff},
DOI = {10.1007/BF01077036},
NOTE={translated in {\it Funct. Anal. Appl.} {\bf 29} (1995), 1--5},
ZBLNUMBER = {0849.16010},
} -
[GJ] E. Getlzer and J. Jones, Operads, homotopy algebra and iterated integrals for double loop spaces.
@misc{GJ,
author={Getlzer, E. and Jones, J.},
TITLE={Operads, homotopy algebra and iterated integrals for double loop spaces},
ARXIV={hep-th/9403055},
} -
[H] D. Huybrechts and M. Nieper-Wisskirchen, "Remarks on derived equivalences of Ricci-flat manifolds," Math. Z., vol. 267, iss. 3-4, pp. 939-963, 2011.
@article {H, MRKEY = {2776067},
AUTHOR = {Huybrechts, Daniel and Nieper-Wisskirchen, Marc},
TITLE = {Remarks on derived equivalences of {R}icci-flat manifolds},
JOURNAL = {Math. Z.},
FJOURNAL = {Mathematische Zeitschrift},
VOLUME = {267},
YEAR = {2011},
NUMBER = {3-4},
PAGES = {939--963},
ISSN = {0025-5874},
CODEN = {MAZEAX},
MRCLASS = {32Q25 (53Cxx)},
MRNUMBER = {2776067},
DOI = {10.1007/s00209-009-0655-z},
ZBLNUMBER = {1213.32012},
} -
[Kapr] M. Kapranov, "Rozansky-Witten invariants via Atiyah classes," Compositio Math., vol. 115, iss. 1, pp. 71-113, 1999.
@article {Kapr, MRKEY = {1671737},
AUTHOR = {Kapranov, M.},
TITLE = {Rozansky-{W}itten invariants via {A}tiyah classes},
JOURNAL = {Compositio Math.},
FJOURNAL = {Compositio Mathematica},
VOLUME = {115},
YEAR = {1999},
NUMBER = {1},
PAGES = {71--113},
ISSN = {0010-437X},
CODEN = {CMPMAF},
MRCLASS = {57R57 (17B70 32J18 53D35 55P48 57M27 57R56)},
MRNUMBER = {1671737},
MRREVIEWER = {Philip A. Foth},
DOI = {10.1023/A:1000664527238},
ZBLNUMBER = {0993.53026},
} -
[K] M. Kontsevich, "Deformation quantization of Poisson manifolds," Lett. Math. Phys., vol. 66, iss. 3, pp. 157-216, 2003.
@article {K, MRKEY = {2062626},
AUTHOR = {Kontsevich, Maxim},
TITLE = {Deformation quantization of {P}oisson manifolds},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics},
VOLUME = {66},
YEAR = {2003},
NUMBER = {3},
PAGES = {157--216},
ISSN = {0377-9017},
CODEN = {LMPHDY},
MRCLASS = {53D55 (16E40 53D17 81S10)},
MRNUMBER = {2062626},
MRREVIEWER = {David Chataur},
DOI = {10.1023/B:MATH.0000027508.00421.bf},
ZBLNUMBER = {1058.53065},
} -
[MT] D. Manchon and C. Torossian, "Cohomologie tangente et cup-produit pour la quantification de Kontsevich," Ann. Math. Blaise Pascal, vol. 10, iss. 1, pp. 75-106, 2003.
@article {MT, MRKEY = {1990011},
AUTHOR = {Manchon, Dominique and Torossian, Charles},
TITLE = {Cohomologie tangente et cup-produit pour la quantification de {K}ontsevich},
JOURNAL = {Ann. Math. Blaise Pascal},
NOTE={French, with English summary},
FJOURNAL = {Annales Mathématiques Blaise Pascal},
VOLUME = {10},
YEAR = {2003},
NUMBER = {1},
PAGES = {75--106},
ISSN = {1259-1734},
MRCLASS = {53D55},
MRNUMBER = {1990011},
MRREVIEWER = {Riccardo Longoni},
URL = {http://ambp.cedram.org/item?id=AMBP_2003__10_1_75_0},
ZBLNUMBER = {1051.53072},
} -
[Mar] N. Markarian, "The Atiyah class, Hochschild cohomology and the Riemann-Roch theorem," J. Lond. Math. Soc., vol. 79, iss. 1, pp. 129-143, 2009.
@article {Mar, MRKEY = {2472137},
AUTHOR = {Markarian, Nikita},
TITLE = {The {A}tiyah class, {H}ochschild cohomology and the {R}iemann-{R}och theorem},
JOURNAL = {J. Lond. Math. Soc.},
FJOURNAL = {Journal of the London Mathematical Society. Second Series},
VOLUME = {79},
YEAR = {2009},
NUMBER = {1},
PAGES = {129--143},
ISSN = {0024-6107},
MRCLASS = {14F05 (13D03 14B10 14C40)},
MRNUMBER = {2472137},
MRREVIEWER = {Cristina Mart{\'ı}nez},
DOI = {10.1112/jlms/jdn064},
ZBLNUMBER = {1167.14005},
} -
[Ram] A. C. Ramadoss, "The Mukai pairing and integral transforms in Hochschild homology," Mosc. Math. J., vol. 10, iss. 3, pp. 629-645, 2010.
@article {Ram, MRKEY = {2732577},
AUTHOR = {Ramadoss, Ajay C.},
TITLE = {The {M}ukai pairing and integral transforms in {H}ochschild homology},
JOURNAL = {Mosc. Math. J.},
FJOURNAL = {Moscow Mathematical Journal},
VOLUME = {10},
YEAR = {2010},
NUMBER = {3},
PAGES = {629--645},
ISSN = {1609-3321},
MRCLASS = {19L10 (14C40 14F05 16E40 19D55)},
MRNUMBER = {2732577},
MRREVIEWER = {L. N. Vaserstein},
ZBLNUMBER = {1208.14013},
URL={http://www.ams.org/distribution/mmj/vol10-3-2010/ramadoss.pdf},
} -
[Sh] B. Shoikhet, "A proof of the Tsygan formality conjecture for chains," Adv. Math., vol. 179, iss. 1, pp. 7-37, 2003.
@article {Sh, MRKEY = {2004726},
AUTHOR = {Shoikhet, Boris},
TITLE = {A proof of the {T}sygan formality conjecture for chains},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {179},
YEAR = {2003},
NUMBER = {1},
PAGES = {7--37},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {53D55 (16S80 18G55)},
MRNUMBER = {2004726},
MRREVIEWER = {Dominique Manchon},
DOI = {10.1016/S0001-8708(02)00023-3},
ZBLNUMBER = {1163.53350},
} -
[Sh1] B. Shoikhet, "Tsygan formality and Duflo formula," Math. Res. Lett., vol. 10, iss. 5-6, pp. 763-775, 2003.
@article {Sh1, MRKEY = {2024732},
AUTHOR = {Shoikhet, Boris},
TITLE = {Tsygan formality and {D}uflo formula},
JOURNAL = {Math. Res. Lett.},
FJOURNAL = {Mathematical Research Letters},
VOLUME = {10},
YEAR = {2003},
NUMBER = {5-6},
PAGES = {763--775},
ISSN = {1073-2780},
MRCLASS = {53D55 (16S80 17B35 18G55)},
MRNUMBER = {2024732},
MRREVIEWER = {Dominique Manchon},
ZBLNUMBER = {1042.17016},
URL={http://www.mathjournals.org/mrl/2003-010-006/2003-010-006-004.html},
} -
[Swan] R. G. Swan, "Hochschild cohomology of quasiprojective schemes," J. Pure Appl. Algebra, vol. 110, iss. 1, pp. 57-80, 1996.
@article {Swan, MRKEY = {1390671},
AUTHOR = {Swan, Richard G.},
TITLE = {Hochschild cohomology of quasiprojective schemes},
JOURNAL = {J. Pure Appl. Algebra},
FJOURNAL = {Journal of Pure and Applied Algebra},
VOLUME = {110},
YEAR = {1996},
NUMBER = {1},
PAGES = {57--80},
ISSN = {0022-4049},
CODEN = {JPAAA2},
MRCLASS = {19D55 (14F99 18G40 18G60)},
MRNUMBER = {1390671},
MRREVIEWER = {Sue Geller},
DOI = {10.1016/0022-4049(95)00091-7},
ZBLNUMBER = {0865.18010},
} -
[Tam] D. Tamarkin, Another proof of M.~Kontsevich formality theorem for $\mathbb{R}^n$, 1998.
@misc{Tam,
author={Tamarkin, D.},
TITLE={Another proof of {M}.~{K}ontsevich formality theorem for $\mathbb{R}^n$},
ARXIV={math.QA/9803025},
YEAR={1998},
} -
[TT] D. Tamarkin and B. Tsygan, "Cyclic formality and index theorems," Lett. Math. Phys., vol. 56, iss. 2, pp. 85-97, 2001.
@article {TT, MRKEY = {1854129},
AUTHOR = {Tamarkin, Dmitry and Tsygan, Boris},
TITLE = {Cyclic formality and index theorems},
NOTE = {EuroConf{é}rence Mosh{é} Flato 2000, Part II (Dijon)},
JOURNAL = {Lett. Math. Phys.},
FJOURNAL = {Letters in Mathematical Physics. A Journal for the Rapid Dissemination of Short Contributions in the Field of Mathematical Physics},
VOLUME = {56},
YEAR = {2001},
NUMBER = {2},
PAGES = {85--97},
ISSN = {0377-9017},
CODEN = {LMPHDY},
MRCLASS = {19K56 (16E40 18D50 19D55 58J22)},
MRNUMBER = {1854129},
MRREVIEWER = {Alexander Gorokhovsky},
DOI = {10.1023/A:1010838604927},
ZBLNUMBER = {1008.19002},
} -
[T] B. Tsygan, "Formality conjectures for chains," in Differential Topology, Infinite-Dimensional Lie Algebras, and Applications, Providence, RI: Amer. Math. Soc., 1999, vol. 194, pp. 261-274.
@incollection {T, MRKEY = {1729368},
AUTHOR = {Tsygan, B.},
TITLE = {Formality conjectures for chains},
BOOKTITLE = {Differential Topology, Infinite-Dimensional {L}ie Algebras, and Applications},
SERIES = {Amer. Math. Soc. Transl. Ser. 2},
VOLUME = {194},
PAGES = {261--274},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1999},
MRCLASS = {53D55 (18G60 58H15)},
MRNUMBER = {1729368},
MRREVIEWER = {Alessandra Frabetti},
ZBLNUMBER = {0962.18008},
} -
[VdB] M. Van den Bergh, "On global deformation quantization in the algebraic case," J. Algebra, vol. 315, iss. 1, pp. 326-395, 2007.
@article {VdB, MRKEY = {2344349},
AUTHOR = {Van den Bergh, Michel},
TITLE = {On global deformation quantization in the algebraic case},
JOURNAL = {J. Algebra},
FJOURNAL = {Journal of Algebra},
VOLUME = {315},
YEAR = {2007},
NUMBER = {1},
PAGES = {326--395},
ISSN = {0021-8693},
CODEN = {JALGA4},
MRCLASS = {14D15 (14F40 16E40)},
MRNUMBER = {2344349},
MRREVIEWER = {Corrado Marastoni},
DOI = {10.1016/j.jalgebra.2007.02.012},
ZBLNUMBER = {1133.14021},
} -
[Xu] P. Xu, "Quantum groupoids," Comm. Math. Phys., vol. 216, iss. 3, pp. 539-581, 2001.
@article {Xu, MRKEY = {1815717},
AUTHOR = {Xu, Ping},
TITLE = {Quantum groupoids},
JOURNAL = {Comm. Math. Phys.},
FJOURNAL = {Communications in Mathematical Physics},
VOLUME = {216},
YEAR = {2001},
NUMBER = {3},
PAGES = {539--581},
ISSN = {0010-3616},
CODEN = {CMPHAY},
MRCLASS = {17B37 (17B62 53D55 58H05 81R50)},
MRNUMBER = {1815717},
MRREVIEWER = {Johannes Huebschmann},
DOI = {10.1007/s002200000334},
ZBLNUMBER = {0986.17003},
} -
[Y] A. Yekutieli, "Deformation quantization in algebraic geometry," Adv. Math., vol. 198, iss. 1, pp. 383-432, 2005.
@article {Y, MRKEY = {2183259},
AUTHOR = {Yekutieli, Amnon},
TITLE = {Deformation quantization in algebraic geometry},
JOURNAL = {Adv. Math.},
FJOURNAL = {Advances in Mathematics},
VOLUME = {198},
YEAR = {2005},
NUMBER = {1},
PAGES = {383--432},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {53D55 (14D15 16S80)},
MRNUMBER = {2183259},
MRREVIEWER = {Hsian-Hua Tseng},
DOI = {10.1016/j.aim.2005.06.009},
ZBLNUMBER = {1085.53081},
} -
[Y1] A. Yekutieli, Private communication.
@misc{Y1,
author={Yekutieli, Amnon},
TITLE = {private communication},
SORTYEAR={2015},
} -
[Y2] A. Yekutieli, "Continuous and twisted $L_\infty$ morphisms," J. Pure Appl. Algebra, vol. 207, iss. 3, pp. 575-606, 2006.
@article {Y2, MRKEY = {2265541},
AUTHOR = {Yekutieli, Amnon},
TITLE = {Continuous and twisted {$L\sb \infty$} morphisms},
JOURNAL = {J. Pure Appl. Algebra},
FJOURNAL = {Journal of Pure and Applied Algebra},
VOLUME = {207},
YEAR = {2006},
NUMBER = {3},
PAGES = {575--606},
ISSN = {0022-4049},
CODEN = {JPAAA2},
MRCLASS = {53D55 (13N15)},
MRNUMBER = {2265541},
DOI = {10.1016/j.jpaa.2005.10.006},
ZBLNUMBER = {1104.53085},
}
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