Geometry & Topology Volume 20, issue 3 (2016)

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The Farrell–Jones conjecture for arbitrary lattices in virtually connected Lie groups

Holger Kammeyer, Wolfgang Lück and Henrik Rüping

Geometry & Topology 20 (2016) 1275–1287

DOI: 10.2140/gt.2016.20.1275

Bibliography

1	R W Bagley, M R Peyrovian, A note on compact subgroups of topological groups, Bull. Austral. Math. Soc. 33 (1986) 273 MR832529
2	A Bartels, T Farrell, W Lück, The Farrell–Jones Conjecture for cocompact lattices in virtually connected Lie groups, (2013) arXiv:1101.0469v2
3	A Bartels, W Lück, On crossed product rings with twisted involutions, their module categories and L–theory, from: "Cohomology of groups and algebraic K–theory" (editors L Ji, K Liu, S T Yau), Adv. Lect. Math. 12, International Press (2010) 1
4	A Bartels, W Lück, The Borel conjecture for hyperbolic and CAT(0)–groups, Ann. of Math. 175 (2012) 631 MR2993750
5	A Bartels, W Lück, H Reich, The K–theoretic Farrell–Jones conjecture for hyperbolic groups, Invent. Math. 172 (2008) 29 MR2385666
6	A Bartels, W Lück, H Reich, On the Farrell–Jones conjecture and its applications, J. Topol. 1 (2008) 57 MR2365652
7	A Bartels, W Lück, H Reich, H Rüping, K– and L–theory of group rings over GL_n(ℤ), Publ. Math. Inst. Hautes Études Sci. 119 (2014) 97
8	A Bartels, H Reich, Coefficients for the Farrell–Jones conjecture, Adv. Math. 209 (2007) 337 MR2294225
9	A Borel, Compact Clifford–Klein forms of symmetric spaces, Topology 2 (1963) 111 MR0146301
10	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
11	Y Choi, Are maximal connected semisimple subgroups automatically closed?, MathOverflow (2013)
12	P Deligne, G D Mostow, Monodromy of hypergeometric functions and nonlattice integral monodromy, Inst. Hautes Études Sci. Publ. Math. (1986) 5 MR849651
13	F T Farrell, L E Jones, Isomorphism conjectures in algebraic K–theory, J. Amer. Math. Soc. 6 (1993) 249 MR1179537
14	F T Farrell, L E Jones, Rigidity for aspherical manifolds with π₁ ⊂ GL_m(ℝ), Asian J. Math. 2 (1998) 215 MR1639544
15	E Formanek, C Procesi, The automorphism group of a free group is not linear, J. Algebra 149 (1992) 494 MR1172442
16	H Garland, M S Raghunathan, Fundamental domains for lattices in (ℝ–)rank 1 semisimple Lie groups, Ann. of Math. 92 (1970) 279 MR0267041
17	F P Greenleaf, M Moskowitz, Finiteness results for lattices in certain Lie groups, Ark. Mat. 48 (2010) 311 MR2672612
18	F P Greenleaf, M Moskowitz, L P Rothschild, Unbounded conjugacy classes in Lie groups and location of central measures, Acta Math. 132 (1974) 225 MR0425035
19	S Helgason, Differential geometry, Lie groups, and symmetric spaces, 34, Amer. Math. Soc. (2001) MR1834454
20	W Lück, K– and L–theory of group rings, from: "Proceedings of the International Congress of Mathematicians, II" (editors R Bhatia, A Pal, G Rangarajan, V Srinivas, M Vanninathan), Hindustan Book Agency (2010) 1071 MR2827832
21	W Lück, H Reich, The Baum–Connes and the Farrell–Jones conjectures in K– and L–theory, from: "Handbook of K–theory, I, II" (editors E M Friedlander, D R Grayson), Springer (2005) 703 MR2181833
22	G A Margulis, Arithmeticity of the irreducible lattices in the semisimple groups of rank greater than 1, Invent. Math. 76 (1984) 93 MR739627
23	G A Margulis, Discrete subgroups of semisimple Lie groups, 17, Springer (1991) MR1090825
24	A L Onishchik, Lie groups and Lie algebras, I, 20, Springer (1993)
25	V Platonov, A Rapinchuk, Algebraic groups and number theory, 139, Academic Press (1994) MR1278263
26	M S Raghunathan, Discrete subgroups of Lie groups, 68, Springer (1972) MR0507234
27	D L Ragozin, A normal subgroup of a semisimple Lie group is closed, Proc. Amer. Math. Soc. 32 (1972) 632 MR0294563
28	H Rüping, The Farrell–Jones conjecture for S–arithmetic groups, J. Topol. 9 (2016) 51 MR3465840
29	A N Starkov, A counterexample to a theorem on lattices in Lie groups, Vestnik Moskov. Univ. Ser. I Mat. Mekh. (1984) 68 MR764036
30	V S Varadarajan, Lie groups, Lie algebras, and their representations, Prentice-Hall (1974) MR0376938
31	E B Vinberg, V V Gorbatsevich, O V Shvartsman, Discrete subgroups of Lie groups, from: "Lie groups and Lie algebras, II" (editor E B Vinberg), Encyclopaedia Math. Sci. 21, Springer (2000) 1, 217 MR1756407
32	C Wegner, The K–theoretic Farrell–Jones conjecture for CAT(0)–groups, Proc. Amer. Math. Soc. 140 (2012) 779 MR2869063
33	C Wegner, The Farrell–Jones conjecture for virtually solvable groups, (2013) arXiv:1308.2432v2
34	H Whitney, Elementary structure of real algebraic varieties, Ann. of Math. 66 (1957) 545 MR0095844
35	T S Wu, A note on a theorem on lattices in Lie groups, Canad. Math. Bull. 31 (1988) 190