Abstract
We prove the Borel Conjecture for a class of groups containing word-hyperbolic groups and groups acting properly, isometrically and cocompactly on a finite-dimensional CAT(0)-space.
-
[Alibegovic+Bestvina(2006)]
E. Alibegović and M. Bestvina, "Limit groups are $ CAT(0)$," J. London Math. Soc., vol. 74, iss. 1, pp. 259-272, 2006.
@article {Alibegovic+Bestvina(2006), MRKEY = {2254564},
AUTHOR = {Alibegovi{ć},
Emina and Bestvina, Mladen},
TITLE = {Limit groups are {$\rm CAT(0)$}},
JOURNAL = {J. London Math. Soc.},
FJOURNAL = {Journal of the London Mathematical Society. Second Series},
VOLUME = {74},
YEAR = {2006},
NUMBER = {1},
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ISSN = {0024-6107},
CODEN = {JLMSAK},
MRCLASS = {57M07 (20F65)},
MRNUMBER = {2254564},
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TITLE={Examples of random groups},
YEAR={2008},
NOTE={preprint},
} -
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A. Bartels, S. Echterhoff, and W. Lück, "Inheritance of isomorphism conjectures under colimits," in $K$-Theory and Noncommutative Geometry, Eur. Math. Soc., Zürich, 2008, pp. 41-70.
@incollection {Bartels-Echterhoff-Lueck(2008colim), MRKEY = {2513332},
AUTHOR = {Bartels, Arthur and Echterhoff, Siegfried and L{ü}ck, Wolfgang},
TITLE = {Inheritance of isomorphism conjectures under colimits},
BOOKTITLE = {{$K$}-Theory and Noncommutative Geometry},
SERIES = {EMS Ser. Congr. Rep.},
PAGES = {41--70},
PUBLISHER = {Eur. Math. Soc., Zürich},
YEAR = {2008},
MRCLASS = {55N20 (19D10 19K56)},
MRNUMBER = {2513332},
MRREVIEWER = {Paul D. Mitchener},
DOI = {10.4171/060-1/2},
ZBLNUMBER = {1159.19005},
} -
[Bartels-Farrell-Jones-Reich(2004)]
A. Bartels, T. Farrell, L. Jones, and H. Reich, "On the isomorphism conjecture in algebraic $K$-theory," Topology, vol. 43, iss. 1, pp. 157-213, 2004.
@article {Bartels-Farrell-Jones-Reich(2004), MRKEY = {2030590},
AUTHOR = {Bartels, Arthur and Farrell, Tom and Jones, Lowell and Reich, Holger},
TITLE = {On the isomorphism conjecture in algebraic {$K$}-theory},
JOURNAL = {Topology},
FJOURNAL = {Topology. An International Journal of Mathematics},
VOLUME = {43},
YEAR = {2004},
NUMBER = {1},
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ISSN = {0040-9383},
CODEN = {TPLGAF},
MRCLASS = {19D50 (19A31 19B28)},
MRNUMBER = {2030590},
MRREVIEWER = {Stanis{\l}aw Betley},
DOI = {10.1016/S0040-9383(03)00032-6},
ZBLNUMBER = {1036.19003},
} -
[Bartels-Lueck(2009coeff)] A. Bartels and W. Lück, "On crossed product rings with twisted involutions, their module categories and $L$-theory," in Cohomology of Groups and algebraic $K$-Theory, Int. Press, Somerville, MA, 2010, vol. 12, pp. 1-54.
@incollection {Bartels-Lueck(2009coeff), MRKEY = {2655174},
AUTHOR = {Bartels, Arthur and L{ü}ck, Wolfgang},
TITLE = {On crossed product rings with twisted involutions, their module categories and {$L$}-theory},
BOOKTITLE = {Cohomology of Groups and algebraic {$K$}-Theory},
SERIES = {Adv. Lect. Math. (ALM)},
VOLUME = {12},
PAGES = {1--54},
PUBLISHER = {Int. Press, Somerville, MA},
YEAR = {2010},
MRCLASS = {19G24 (18F25 57R67)},
MRNUMBER = {2655174},
ZBLNUMBER = {1205.19006},
} -
[Bartels-Lueck(2010CAT(0)flow)] A. Bartels and W. Lück, Geodesic flow for CAT(0)-groups, 2010.
@misc{Bartels-Lueck(2010CAT(0)flow),
author={Bartels, Arthur and L{ü}ck, Wolfgang},
TITLE = {Geodesic flow for {C}{A}{T}(0)-groups},
YEAR={2010},
NOTE={preprint},
ARXIV={1003.4630v1},
} -
[Bartels-Lueck-Reich(2008cover)]
A. Bartels, W. Lück, and H. Reich, "Equivariant covers for hyperbolic groups," Geom. Topol., vol. 12, iss. 3, pp. 1799-1882, 2008.
@article {Bartels-Lueck-Reich(2008cover), MRKEY = {2421141},
AUTHOR = {Bartels, Arthur and L{ü}ck, Wolfgang and Reich, Holger},
TITLE = {Equivariant covers for hyperbolic groups},
JOURNAL = {Geom. Topol.},
FJOURNAL = {Geometry \& Topology},
VOLUME = {12},
YEAR = {2008},
NUMBER = {3},
PAGES = {1799--1882},
ISSN = {1465-3060},
MRCLASS = {20F67 (20F65 37D40 57M07)},
MRNUMBER = {2421141},
MRREVIEWER = {Vassilis Metaftsis},
DOI = {10.2140/gt.2008.12.1799},
ZBLNUMBER = {1185.20045},
} -
[Bartels-Lueck-Reich(2008hyper)]
A. Bartels, W. Lück, and H. Reich, "The $K$-theoretic Farrell-Jones conjecture for hyperbolic groups," Invent. Math., vol. 172, iss. 1, pp. 29-70, 2008.
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AUTHOR = {Bartels, Arthur and L{ü}ck, Wolfgang and Reich, Holger},
TITLE = {The {$K$}-theoretic {F}arrell-{J}ones conjecture for hyperbolic groups},
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DOI = {10.1112/jtopol/jtm008},
ZBLNUMBER = {1141.19002},
} -
[Bartels-Lueck-Weinberger(2010)]
A. Bartels, W. Lück, and S. Weinberger, "On hyperbolic groups with spheres as boundary," J. Differential Geom., vol. 86, iss. 1, pp. 1-16, 2010.
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FJOURNAL = {Journal of Differential Geometry},
VOLUME = {86},
YEAR = {2010},
NUMBER = {1},
PAGES = {1--16},
ISSN = {0022-040X},
CODEN = {JDGEAS},
MRCLASS = {57M07 (20F67)},
MRNUMBER = {2772544},
MRREVIEWER = {Igor V. Nikolaev},
URL = {http://projecteuclid.org/getRecord?id=euclid.jdg/1299766682},
ZBLNUMBER = {1216.53043},
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TITLE = {Coefficients for the {F}arrell-{J}ones conjecture},
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FJOURNAL = {Advances in Mathematics},
VOLUME = {209},
YEAR = {2007},
NUMBER = {1},
PAGES = {337--362},
ISSN = {0001-8708},
CODEN = {ADMTA4},
MRCLASS = {19D50 (19J10 20F67 57R80)},
MRNUMBER = {2294225},
MRREVIEWER = {Stratos Prassidis},
DOI = {10.1016/j.aim.2006.05.005},
ZBLNUMBER = {1161.19003},
} -
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VOLUME = {28},
YEAR = {2003},
NUMBER = {1},
PAGES = {19--37},
ISSN = {0920-3036},
CODEN = {KTHEEO},
MRCLASS = {19D50 (19A31 19B28 19D55 19E20)},
MRNUMBER = {1988817},
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AUTHOR = {Bestvina, Mladen and Mess, Geoffrey},
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TITLE={{A}lgebraic {$K$}-theory over the infinite dihedral group: a controlled topology approach},
JOURNAL={J. Topol.},
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AUTHOR = {Davis, Michael W.},
TITLE = {The Geometry and Topology of {C}oxeter Groups},
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ADDRESS = {Princeton, NJ},
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ISBN = {978-0-691-13138-2; 0-691-13138-4},
MRCLASS = {20F55 (05B45 05C25 51-02 57M07)},
MRNUMBER = {2360474},
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AUTHOR = {Farrell, F. T. and Jones, L. E.},
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MRREVIEWER = {Christopher W. Stark},
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AUTHOR = {Farrell, F. T. and Jones, L. E.},
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@incollection {Farrell-Jones(1993c), MRKEY = {1216623},
AUTHOR = {Farrell, F. T. and Jones, L. E.},
TITLE = {Topological rigidity for compact non-positively curved manifolds},
BOOKTITLE = {Differential Geometry: {R}iemannian Geometry},
VENUE={{L}os {A}ngeles, {CA},
1990},
SERIES = {Proc. Sympos. Pure Math.},
VOLUME = {54},
PAGES = {229--274},
PUBLISHER = {Amer. Math. Soc.},
ADDRESS = {Providence, RI},
YEAR = {1993},
MRCLASS = {57R65 (53C21 57R67 57S30)},
MRNUMBER = {1216623},
MRREVIEWER = {Christopher W. Stark},
ZBLNUMBER = {0796.53043},
} -
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AUTHOR = {Farrell, F. T. and Jones, L. E.},
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VOLUME = {2},
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NUMBER = {2},
PAGES = {215--262},
ISSN = {1093-6106},
MRCLASS = {57R57 (53C20)},
MRNUMBER = {1639544},
MRREVIEWER = {A. A. Ranicki},
ZBLNUMBER = {0912.57012},
} -
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AUTHOR = {Freedman, Michael H.},
TITLE = {The disk theorem for four-dimensional manifolds},
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VENUE={{W}arsaw, 1983},
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PUBLISHER = {PWN},
ADDRESS = {Warsaw},
YEAR = {1984},
MRCLASS = {57N15 (57R65)},
MRNUMBER = {0804721},
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} -
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W. Lück, "$K$- and $L$-theory of the semi-direct product of the discrete 3-dimensional Heisenberg group by ${\Bbb Z}/4$," Geom. Topol., vol. 9, pp. 1639-1676, 2005.
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SERIES = {Lecture Notes in Math.},
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VENUE={{N}ew {B}runswick, {N}.{J}., 1983},
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[Ranicki(1992)] A. A. Ranicki, Algebraic $L$-Theory and Topological Manifolds, Cambridge: Cambridge Univ. Press, 1992, vol. 102.
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A. Ranicki, Lower $K$- and $L$-Theory, Cambridge: Cambridge Univ. Press, 1992, vol. 178.
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Z. Sela, "Diophantine geometry over groups. I. Makanin-Razborov diagrams," Publ. Math. Inst. Hautes Études Sci., iss. 93, pp. 31-105, 2001.
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}