K- and L-theory of group rings over GLn(𝐙)
Bartels, Arthur1 ; Lück, Wolfgang2 ; Reich, Holger3 ; Rüping, Henrik2
1 Mathematisches Institut, Westfälische Wilhelms-Universität Münster Einsteinstr. 60 48149 Münster Germany
2 Mathematisches Institut, Rheinische Wilhelms-Universität Bonn Endenicher Allee 60 53115 Bonn Germany
3 Institut für Mathematik, Freie Universität Berlin Arnimallee 7 14195 Berlin Germany
Publications Mathématiques de l'IHÉS, Tome 119 (2014), pp. 97-125.

We prove the K- and L-theoretic Farrell-Jones Conjecture (with coefficients in additive categories) for GLn(𝐙)

DOI : 10.1007/s10240-013-0055-0
Mots-clés : Abelian Group, Volume Function, Group Ring, Cyclic Subgroup, Wreath Product
Bartels, Arthur 1 ; Lück, Wolfgang 2 ; Reich, Holger 3 ; Rüping, Henrik 2

1 Mathematisches Institut, Westfälische Wilhelms-Universität Münster Einsteinstr. 60 48149 Münster Germany
2 Mathematisches Institut, Rheinische Wilhelms-Universität Bonn Endenicher Allee 60 53115 Bonn Germany
3 Institut für Mathematik, Freie Universität Berlin Arnimallee 7 14195 Berlin Germany 
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     journal = {Publications Math\'ematiques de l'IH\'ES},
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Bartels, Arthur; Lück, Wolfgang; Reich, Holger; Rüping, Henrik. $K$- and $L$-theory of group rings over $GL_n ( \mathbf{Z} )$. Publications Mathématiques de l'IHÉS, Tome 119 (2014), pp. 97-125. doi : 10.1007/s10240-013-0055-0. https://www.numdam.org/articles/10.1007/s10240-013-0055-0/

[1.] A. Bartels, T. Farrell, and W. Lück, The Farrell-Jones conjecture for cocompact lattices in virtually connected Lie groups. | arXiv

[2.] Bartels, A.; Lück, W. On twisted group rings with twisted involutions, their module categories and L-theory, Cohomology of Groups and Algebraic K-Theory (2009), pp. 1-55 | MR | Zbl

[3.] Bartels, A.; Lück, W. Geodesic flow for CAT(0)-groups, Geom. Topol., Volume 16 (2012), pp. 1345-1391 | DOI | MR | Zbl

[4.] Bartels, A.; Lück, W. The Borel conjecture for hyperbolic and CAT(0)-groups, Ann. Math. (2), Volume 175 (2012), pp. 631-689 | DOI | MR | Zbl

[5.] Bartels, A.; Lück, W.; Reich, H. The K-theoretic Farrell-Jones conjecture for hyperbolic groups, Invent. Math., Volume 172 (2008), pp. 29-70 | DOI | MR | Zbl

[6.] Bartels, A.; Lück, W.; Reich, H. On the Farrell-Jones conjecture and its applications, Topology, Volume 1 (2008), pp. 57-86 | DOI | MR | Zbl

[7.] Bartels, A.; Reich, H. Coefficients for the Farrell-Jones conjecture, Adv. Math., Volume 209 (2007), pp. 337-362 | DOI | MR | Zbl

[8.] Bridson, M. R.; Haefliger, A. Metric Spaces of Non-Positive Curvature (1999) | MR | Zbl

[9.] Brown, K. S. Cohomology of Groups (1982) | MR | Zbl

[10.] Davis, J. F.; Quinn, F.; Reich, H. Algebraic K-theory over the infinite dihedral group: a controlled topology approach, Topology, Volume 4 (2011), pp. 505-528 | DOI | MR | Zbl

[11.] Dixon, J. D.; Mortimer, B. Permutation Groups (1996) | MR | Zbl

[12.] Eberlein, P. B. Geometry of Nonpositively Curved Manifolds (1996) | MR | Zbl

[13.] Farrell, F. T.; Jones, L. E. Isomorphism conjectures in algebraic K-theory, J. Am. Math. Soc., Volume 6 (1993), pp. 249-297 | MR | Zbl

[14.] Farrell, F. T.; Jones, L. E. Rigidity for aspherical manifolds with π1⊂GLm(R), Asian J. Math., Volume 2 (1998), pp. 215-262 | MR | Zbl

[15.] Farrell, F. T.; Roushon, S. K. The Whitehead groups of braid groups vanish, Int. Math. Res. Not., Volume 10 (2000), pp. 515-526 | DOI | MR | Zbl

[16.] Grayson, D. R. Reduction theory using semistability, Comment. Math. Helv., Volume 59 (1984), pp. 600-634 | DOI | MR | Zbl

[17.] Griffiths, P.; Harris, J. Principles of Algebraic Geometry (1978) | MR | Zbl

[18.] Helgason, S. Differential Geometry, Lie Groups, and Symmetric Spaces (1978) | MR | Zbl

[19.] P. Kühl, Isomorphismusvermutungen und 3-Mannigfaltigkeiten. Preprint, | arXiv

[20.] Lück, W. Survey on classifying spaces for families of subgroups, Infinite Groups: Geometric, Combinatorial and Dynamical Aspects (2005), pp. 269-322 | MR | Zbl

[21.] Lück, W.; Reich, H. The Baum-Connes and the Farrell-Jones conjectures in K- and L-theory, Handbook of K-Theory, vols. 1, 2 (2005), pp. 703-842 | MR | Zbl

[22.] Neukirch, J. Algebraic Number Theory (1999) | MR | Zbl

[23.] Roushon, S. K. The Farrell-Jones isomorphism conjecture for 3-manifold groups, K-Theory, Volume 1 (2008), pp. 49-82 | MR | Zbl

[24.] Wegner, C. The K-theoretic Farrell-Jones conjecture for CAT(0)-groups, Proc. Am. Math. Soc., Volume 140 (2012), pp. 779-793 | DOI | MR | Zbl

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  • Hebestreit, Fabian; Land, Markus; Nikolaus, Thomas On the homotopy type of L‐spectra of the integers, Journal of Topology, Volume 14 (2021) no. 1, p. 183 | DOI:10.1112/topo.12180
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  • Lück, Wolfgang; Reich, Holger; Rognes, John; Varisco, Marco Algebraic K-theory of group rings and the cyclotomic trace map, Advances in Mathematics, Volume 304 (2017), p. 930 | DOI:10.1016/j.aim.2016.09.004
  • Bartels, A. Coarse flow spaces for relatively hyperbolic groups, Compositio Mathematica, Volume 153 (2017) no. 4, p. 745 | DOI:10.1112/s0010437x16008216
  • Kammeyer, Holger; Lück, Wolfgang; Rüping, Henrik The Farrell–Jones conjecture for arbitrary lattices in virtually connected Lie groups, Geometry Topology, Volume 20 (2016) no. 3, p. 1275 | DOI:10.2140/gt.2016.20.1275
  • Rüping, H. The Farrell–Jones conjecture forS-arithmetic groups, Journal of Topology, Volume 9 (2016) no. 1, p. 51 | DOI:10.1112/jtopol/jtv034
  • Winges, Christoph On the transfer reducibility of certain Farrell–Hsiang groups, Algebraic Geometric Topology, Volume 15 (2015) no. 5, p. 2921 | DOI:10.2140/agt.2015.15.2921
  • Wegner, Christian The Farrell–Jones conjecture for virtually solvable groups:, Journal of Topology, Volume 8 (2015) no. 4, p. 975 | DOI:10.1112/jtopol/jtv026
  • Lück, Wolfgang Some Open Problems About Aspherical Closed Manifolds, Trends in Contemporary Mathematics, Volume 8 (2014), p. 33 | DOI:10.1007/978-3-319-05254-0_3

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