Algebraic & Geometric Topology Volume 14, issue 4 (2014)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the Journal

Editorial Board

Subscriptions

Submission Guidelines

Submission Page

Policies for Authors

Ethics Statement

ISSN 1472-2739 (online)

ISSN 1472-2747 (print)

Author Index

To Appear

Other MSP Journals

$L^{2}$–invariants of nonuniform lattices in semisimple Lie groups

Holger Kammeyer

Algebraic & Geometric Topology 14 (2014) 2475–2509

DOI: 10.2140/agt.2014.14.2475

Bibliography

1	A Adem, Y Ruan, Twisted orbifold $K\!$–theory, Comm. Math. Phys. 237 (2003) 533 MR1993337
2	R C Alperin, An elementary account of Selberg's lemma, Enseign. Math. 33 (1987) 269 MR925989
3	A Borel, Introduction aux groupes arithmétiques, Publ. Inst. Math. Univ. Strasbourg 1341, Hermann (1969) 125 MR0244260
4	A Borel, The $L^2$–cohomology of negatively curved Riemannian symmetric spaces, Ann. Acad. Sci. Fenn. Ser. A I Math. 10 (1985) 95 MR802471
5	A Borel, Linear algebraic groups, Graduate Texts in Mathematics 126, Springer (1991) MR1102012
6	A Borel, Harish-Chandra, Arithmetic subgroups of algebraic groups, Ann. of Math. 75 (1962) 485 MR0147566
7	A Borel, L Ji, Compactifications of locally symmetric spaces, J. Differential Geom. 73 (2006) 263 MR2226955
8	A Borel, L Ji, Compactifications of symmetric and locally symmetric spaces, Birkhäuser (2006) MR2189882
9	A Borel, J P Serre, Corners and arithmetic groups, Comment. Math. Helv. 48 (1973) 436 MR0387495
10	A Borel, N R Wallach, Continuous cohomology, discrete subgroups, and representations of reductive groups, Annals of Mathematics Studies 94, Princeton Univ. Press (1980) MR554917
11	D Burghelea, L Friedlander, T Kappeler, P McDonald, Analytic and Reidemeister torsion for representations in finite type Hilbert modules, Geom. Funct. Anal. 6 (1996) 751 MR1415762
12	J Cheeger, M Gromov, Bounds on the von Neumann dimension of $L^2$–cohomology and the Gauss–Bonnet theorem for open manifolds, J. Differential Geom. 21 (1985) 1 MR806699
13	J Cheeger, M Gromov, $L_2$–cohomology and group cohomology, Topology 25 (1986) 189 MR837621
14	T tom Dieck, Transformation groups, de Gruyter Studies in Mathematics 8, de Gruyter (1987) MR889050
15	J Dodziuk, de Rham–Hodge theory for $L^{2}$–cohomology of infinite coverings, Topology 16 (1977) 157 MR0445560
16	A V Efremov, Cell decompositions and the Novikov–Shubin invariants, Uspekhi Mat. Nauk 46 (1991) 189 MR1134099
17	A Furman, Gromov's measure equivalence and rigidity of higher rank lattices, Ann. of Math. 150 (1999) 1059 MR1740986
18	D Gaboriau, Invariants $l^2$ de relations d'équivalence et de groupes, Publ. Math. Inst. Hautes Études Sci. (2002) 93 MR1953191
19	D Gaboriau, Examples of groups that are measure equivalent to the free group, Ergodic Theory Dynam. Systems 25 (2005) 1809 MR2183295
20	M Goresky, G Harder, R MacPherson, Weighted cohomology, Invent. Math. 116 (1994) 139 MR1253192
21	Y Guivarch, Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973) 333 MR0369608
22	Harish-Chandra, Automorphic forms on semisimple Lie groups, Notes by J. G. M. Mars. Lecture Notes in Mathematics 62, Springer (1968) MR0232893
23	E Hess, T Schick, $L^2$–torsion of hyperbolic manifolds, Manuscripta Math. 97 (1998) 329 MR1654784
24	L Ji, Integral Novikov conjectures and arithmetic groups containing torsion elements, Comm. Anal. Geom. 15 (2007) 509 MR2379803
25	H Kammeyer, $L^2$–invariants of nonuniform lattices in semisimple Lie groups, PhD thesis, Universität Göttingen (2013)
26	H Kang, Cofinite classifying spaces for lattices in R–rank one semisimple Lie groups, PhD thesis, University of Michigan (2011)
27	J Lott, Heat kernels on covering spaces and topological invariants, J. Differential Geom. 35 (1992) 471 MR1158345
28	J Lott, W Lück, $L^2$–topological invariants of $3$–manifolds, Invent. Math. 120 (1995) 15 MR1323981
29	W Lück, Dimension theory of arbitrary modules over finite von Neumann algebras and $L^2$–Betti numbers, I: Foundations, J. Reine Angew. Math. 495 (1998) 135 MR1603853
30	W Lück, $L^2$–invariants: Theory and applications to geometry and $K\!$–theory, Ergeb. Math. Grenzgeb. 44, Springer (2002) MR1926649
31	W Lück, H Reich, T Schick, Novikov–Shubin invariants for arbitrary group actions and their positivity, from: "Tel Aviv Topology Conference: Rothenberg Festschrift" (editors M Farber, W Lück, S Weinberger), Contemp. Math. 231, Amer. Math. Soc. (1999) 159 MR1707342
32	W Lück, R Sauer, C Wegner, $L^2$–torsion, the measure-theoretic determinant conjecture, and uniform measure equivalence, J. Topol. Anal. 2 (2010) 145 MR2652905
33	W Lück, T Schick, $L^2$–torsion of hyperbolic manifolds of finite volume, Geom. Funct. Anal. 9 (1999) 518 MR1708444
34	G A Margulis, Arithmeticity of the irreducible lattices in the semisimple groups of rank greater than $1$, Invent. Math. 76 (1984) 93 MR739627
35	M Olbrich, $L^2$–invariants of locally symmetric spaces, Doc. Math. 7 (2002) 219 MR1938121
36	M Rumin, Differential geometry on C–C spaces and application to the Novikov–Shubin numbers of nilpotent Lie groups, C. R. Acad. Sci. Paris Sér. I Math. 329 (1999) 985 MR1733906
37	M Rumin, Around heat decay on forms and relations of nilpotent Lie groups, Sémin. Théor. Spectr. Géom. 19, Univ. Grenoble I (2001) 123 MR1909080
38	T Schick, $L^2$–determinant class and approximation of $L^2$–Betti numbers, Trans. Amer. Math. Soc. 353 (2001) 3247 MR1828605
39	J Tits, Classification of algebraic semisimple groups, from: "Algebraic Groups and Discontinuous Subgroups", Amer. Math. Soc. (1966) 33 MR0224710
40	C T C Wall, Rational Euler characteristics, Proc. Cambridge Philos. Soc. 57 (1961) 182 MR0122853
41	C Wegner, $L^2$–invariants of finite aspherical CW–complexes with fundamental group containing a non-trivial elementary amenable normal subgroup, Schriftenreihe Math. Inst. Univ. Münster 3. Ser. 28, Univ. Münster (2000) 3 MR1851963
42	C Wegner, $L^2$–invariants of finite aspherical CW–complexes, Manuscripta Math. 128 (2009) 469 MR2487437
43	D Witte Morris, Introduction to arithmetic groups, (2012) arXiv:math/0106063v4