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Dynamic characterizations of quasi-isometry and applications to cohomology

Xin Li

Algebraic & Geometric Topology 18 (2018) 3477–3535
Bibliography
1 V Alekseev, M Finn-Sell, Sofic boundaries of groups and coarse geometry of sofic approximations, preprint (2017) arXiv:1608.02242v2
2 J M Alonso, Finiteness conditions on groups and quasi-isometries, J. Pure Appl. Algebra 95 (1994) 121 MR1293049
3 B Bekka, P de la Harpe, A Valette, Kazhdan’s property (T), 11, Cambridge Univ. Press (2008) MR2415834
4 R Bieri, On groups of finite cohomological dimension and duality groups over a ring, J. Pure Appl. Algebra 6 (1975) 83 MR0374287
5 R Bieri, Homological dimension of discrete groups, Mathematics Department, Queen Mary College (1976) MR0466344
6 M Blank, F Diana, Uniformly finite homology and amenable groups, Algebr. Geom. Topol. 15 (2015) 467 MR3325745
7 J Block, S Weinberger, Aperiodic tilings, positive scalar curvature and amenability of spaces, J. Amer. Math. Soc. 5 (1992) 907 MR1145337
8 M Bourdon, F Martin, A Valette, Vanishing and non-vanishing for the first Lp–cohomology of groups, Comment. Math. Helv. 80 (2005) 377 MR2142247
9 J Brodzki, G A Niblo, N Wright, Pairings, duality, amenability and bounded cohomology, J. Eur. Math. Soc. 14 (2012) 1513 MR2966657
10 K S Brown, Cohomology of groups, 87, Springer (1982) MR672956
11 T M Carlsen, E Ruiz, A Sims, Equivalence and stable isomorphism of groupoids, and diagonal-preserving stable isomorphisms of graph C–algebras and Leavitt path algebras, Proc. Amer. Math. Soc. 145 (2017) 1581 MR3601549
12 M Crainic, I Moerdijk, A homology theory for étale groupoids, J. Reine Angew. Math. 521 (2000) 25 MR1752294
13 K Das, From the geometry of box spaces to the geometry and measured couplings of groups, J. Topol. Anal. 10 (2018) 401 MR3809593
14 M W Davis, Poincaré duality groups, from: "Surveys on surgery theory, I" (editors S Cappell, A Ranicki, J Rosenberg), Ann. of Math. Stud. 145, Princeton Univ. Press (2000) 167 MR1747535
15 T Delabie, A Khukhro, Coarse fundamental groups and box spaces, preprint (2017) arXiv:1701.02919
16 F Dembegioti, O Talelli, On some examples of duality groups, Arch. Math. (Basel) 90 (2008) 304 MR2390294
17 C Druţu, M Kapovich, Geometric group theory, 63, Amer. Math. Soc. (2018) MR3753580
18 G Elek, Coarse cohomology and lp–cohomology, K–Theory 13 (1998) 1 MR1610246
19 A Furman, Orbit equivalence rigidity, Ann. of Math. 150 (1999) 1083 MR1740985
20 G Gandini, Cohomological invariants and the classifying space for proper actions, Groups Geom. Dyn. 6 (2012) 659 MR2996406
21 S M Gersten, Quasi-isometry invariance of cohomological dimension, C. R. Acad. Sci. Paris Sér. I Math. 316 (1993) 411 MR1209258
22 M Gromov, Asymptotic invariants of infinite groups, from: "Geometric group theory, II" (editors G A Niblo, M A Roller), London Math. Soc. Lecture Note Ser. 182, Cambridge Univ. Press (1993) 1 MR1253544
23 A Guichardet, Cohomologie des groupes topologiques et des algèbres de Lie, 2, CEDIC (1980) MR644979
24 A Haefliger, Differential cohomology, from: "Differential topology", Liguori (1979) 19 MR660658
25 P Jolissaint, Rapidly decreasing functions in reduced C–algebras of groups, Trans. Amer. Math. Soc. 317 (1990) 167 MR943303
26 I Kapovich, A Lukyanenko, Quasi-isometric co-Hopficity of non-uniform lattices in rank-one semi-simple Lie groups, Conform. Geom. Dyn. 16 (2012) 269 MR2983835
27 M Kapovich, B Kleiner, Coarse Alexander duality and duality groups, J. Differential Geom. 69 (2005) 279 MR2168506
28 P H Kropholler, On groups of type (FP), J. Pure Appl. Algebra 90 (1993) 55 MR1246274
29 I J Leary, Uncountably many groups of type FP, preprint (2017) arXiv:1512.06609v3
30 X Li, Nuclearity of semigroup C–algebras and the connection to amenability, Adv. Math. 244 (2013) 626 MR3077884
31 X Li, Partial transformation groupoids attached to graphs and semigroups, Int. Math. Res. Not. 2017 (2017) 5233 MR3694599
32 X Li, Continuous orbit equivalence rigidity, Ergodic Theory Dynam. Systems 38 (2018) 1543 MR3789176
33 X Li, J Renault, Cartan subalgebras in C–algebras : existence and uniqueness, preprint (2017) arXiv:1703.10505
34 F Martin, A Valette, On the first Lp–cohomology of discrete groups, Groups Geom. Dyn. 1 (2007) 81 MR2294249
35 H Matui, Homology and topological full groups of étale groupoids on totally disconnected spaces, Proc. Lond. Math. Soc. 104 (2012) 27 MR2876963
36 K Medynets, R Sauer, A Thom, Cantor systems and quasi-isometry of groups, Bull. Lond. Math. Soc. 49 (2017) 709 MR3725491
37 S Merenkov, A Sierpiński carpet with the co-Hopfian property, Invent. Math. 180 (2010) 361 MR2609245
38 M Mimura, N Ozawa, H Sako, Y Suzuki, Group approximation in Cayley topology and coarse geometry, III : Geometric property (T), Algebr. Geom. Topol. 15 (2015) 1067 MR3342685
39 I Moerdijk, Classifying toposes and foliations, Ann. Inst. Fourier (Grenoble) 41 (1991) 189 MR1112197
40 L Mosher, M Sageev, K Whyte, Quasi-actions on trees, I : Bounded valence, Ann. of Math. 158 (2003) 115 MR1998479
41 L Mosher, M Sageev, K Whyte, Quasi-actions on trees, II : Finite depth Bass–Serre trees, 1008, Amer. Math. Soc. (2011) MR2867450
42 S I Oguni, l2–invariants of discrete groups under coarse equivalence and l2–invariants of cocompact étale groupoids, preprint (2010)
43 P Pansu, Cohomologie Lp : invariance sous quasiisométries, preprint (1995)
44 H D Petersen, L2–Betti numbers of locally compact groups, PhD thesis, University of Copenhagen (2012) arXiv:1104.3294v3
45 N Petrosyan, Jumps in cohomology and free group actions, J. Pure Appl. Algebra 210 (2007) 695 MR2324601
46 M J Puls, Group cohomology and Lp–cohomology of finitely generated groups, Canad. Math. Bull. 46 (2003) 268 MR1981681
47 J Renault, A groupoid approach to C–algebras, 793, Springer (1980) MR584266
48 J Roe, Lectures on coarse geometry, 31, Amer. Math. Soc. (2003) MR2007488
49 R Sauer, Homological invariants and quasi-isometry, Geom. Funct. Anal. 16 (2006) 476 MR2231471
50 R Sauer, M Schrödl, Vanishing of 2–Betti numbers of locally compact groups as an invariant of coarse equivalence, preprint (2017) arXiv:1702.01685v2
51 Y Shalom, Harmonic analysis, cohomology, and the large-scale geometry of amenable groups, Acta Math. 192 (2004) 119 MR2096453
52 G Skandalis, J L Tu, G Yu, The coarse Baum–Connes conjecture and groupoids, Topology 41 (2002) 807 MR1905840
53 R Strebel, A remark on subgroups of infinite index in Poincaré duality groups, Comment. Math. Helv. 52 (1977) 317 MR0457588
54 J Špakula, R Willett, On rigidity of Roe algebras, Adv. Math. 249 (2013) 289 MR3116573