Geometry & Topology Volume 17, issue 1 (2013)

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ISSN (electronic): 1364-0380

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Noncoherence of arithmetic hyperbolic lattices

Michael Kapovich

Geometry & Topology 17 (2013) 39–71

DOI: 10.2140/gt.2013.17.39

Bibliography

1	I Agol, Systoles of hyperbolic 4–manifolds arXiv:math.GT/0612290
2	I Agol, The virtual Haken conjecture arXiv:1204.2810
3	I Agol, Criteria for virtual fibering, J. Topol. 1 (2008) 269 MR2399130
4	I Agol, D D Long, A W Reid, The Bianchi groups are separable on geometrically finite subgroups, Ann. of Math. 153 (2001) 599 MR1836283
5	G Baumslag, J E Roseblade, Subgroups of direct products of free groups, J. London Math. Soc. 30 (1984) 44 MR760871
6	M Bestvina, N Brady, Morse theory and finiteness properties of groups, Invent. Math. 129 (1997) 445 MR1465330
7	R Bieri, Homological dimension of discrete groups, , Queen Mary College Department of Pure Mathematics (1981) MR715779
8	J S Birman, A Lubotzky, J McCarthy, Abelian and solvable subgroups of the mapping class groups, Duke Math. J. 50 (1983) 1107 MR726319
9	B H Bowditch, G Mess, A 4–dimensional Kleinian group, Trans. Amer. Math. Soc. 344 (1994) 391 MR1240944
10	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
11	K Corlette, Archimedean superrigidity and hyperbolic geometry, Ann. of Math. 135 (1992) 165 MR1147961
12	P Deligne, G D Mostow, Commensurabilities among lattices in PU(1,n), 132, Princeton Univ. Press (1993) MR1241644
13	T Delzant, L’invariant de Bieri–Neumann–Strebel des groupes fondamentaux des variétés kählériennes, Math. Ann. 348 (2010) 119 MR2657436
14	R Gitik, Doubles of groups and hyperbolic LERF 3–manifolds, Ann. of Math. 150 (1999) 775 MR1740992
15	R Gitik, Ping-pong on negatively curved groups, J. Algebra 217 (1999) 65 MR1700476
16	M Gromov, R Schoen, Harmonic maps into singular spaces and p–adic superrigidity for lattices in groups of rank one, Inst. Hautes Études Sci. Publ. Math. (1992) 165 MR1215595
17	F J Grunewald, On some groups which cannot be finitely presented, J. London Math. Soc. 17 (1978) 427 MR500627
18	F Haglund, Finite index subgroups of graph products, Geom. Dedicata 135 (2008) 167 MR2413337
19	F Haglund, J Światkowski, Separating quasi-convex subgroups in 7–systolic groups, Groups Geom. Dyn. 2 (2008) 223 MR2393180
20	M Hall Jr., Coset representations in free groups, Trans. Amer. Math. Soc. 67 (1949) 421 MR0032642
21	J Hillman, Private communication (1998)
22	J A Hillman, Complex surfaces which are fibre bundles, Topology Appl. 100 (2000) 187 MR1733043
23	J A Hillman, Four-manifolds, geometries and knots, 5 (2002) MR1943724
24	J A Hillman, D H Kochloukova, Finiteness conditions and PD_r–group covers of PD_n–complexes, Math. Z. 256 (2007) 45 MR2282258
25	M Kapovich, On normal subgroups in the fundamental groups of complex surfaces (1998) arXiv:1204.2810
26	M Kapovich, Representations of polygons of finite groups, Geom. Topol. 9 (2005) MR2175160
27	M Kapovich, L Potyagailo, On the absence of Ahlfors’ finiteness theorem for Kleinian groups in dimension three, Topology Appl. 40 (1991) 83 MR1114093
28	M Kapovich, L Potyagailo, E Vinberg, Noncoherence of some lattices in Isom(ℍⁿ), from: "The Zieschang Gedenkschrift" (editors M Boileau, M Scharlemann, R Weidmann), Geom. Topol. Monogr., Geom. Topol. Publ., Coventry (2008) 335 MR2484708
29	D Kazhdan, Some applications of the Weil representation, J. Analyse Mat. 32 (1977) 235 MR0492089
30	J S Li, J J Millson, On the first Betti number of a hyperbolic manifold with an arithmetic fundamental group, Duke Math. J. 71 (1993) 365 MR1233441
31	K Liu, Geometric height inequalities, Math. Res. Lett. 3 (1996) 693 MR1418581
32	D D Long, G A Niblo, Subgroup separability and 3–manifold groups, Math. Z. 207 (1991) 209 MR1109662
33	C Maclachlan, A W Reid, The arithmetic of hyperbolic 3–manifolds, 219, Springer (2003) MR1937957
34	D McReynolds, Arithmetic lattices in SU(n,1) (2007)
35	V Platonov, A Rapinchuk, Algebraic groups and number theory, 139, Academic Press (1994) MR1278263
36	L Potyagaĭlo, The problem of finiteness for Kleinian groups in 3–space, from: "Knots 90" (editor A Kawauchi), de Gruyter (1992) 619 MR1177449
37	L Potyagaĭlo, Finitely generated Kleinian groups in 3–space and 3–manifolds of infinite homotopy type, Trans. Amer. Math. Soc. 344 (1994) 57 MR1250823
38	J D Rogawski, Automorphic representations of unitary groups in three variables, 123, Princeton Univ. Press (1990) MR1081540
39	G P Scott, Compact submanifolds of 3–manifolds, J. London Math. Soc. (2) 7 (1973) 246 MR0326737
40	G Scott, Subgroups of surface groups are almost geometric, J. London Math. Soc. (2) 17 (1978) 555 MR0494062
41	M Stover, Property (FA) and lattices in SU(2,1), Internat. J. Algebra Comput. 17 (2007) 1335 MR2372600
42	È B Vinberg, Discrete groups generated by reflections in Lobačevskiĭ spaces, Mat. Sb. 72 (114) (1967) 471, 303 MR0207853
43	È B Vinberg, O V Shvartsman, Discrete groups of motions of spaces of constant curvature, from: "Geometry, II", Encyclopaedia Math. Sci. 29, Springer (1993) 139 MR1254933
44	C Wall, List of problems, from: "Homological group theory" (editor C T C Wall), London Math. Soc. Lecture Note Ser. 36, Cambridge Univ. Press (1979) 369 MR564438
45	N R Wallach, Square integrable automorphic forms and cohomology of arithmetic quotients of SU(p,q), Math. Ann. 266 (1984) 261 MR730169
46	D T Wise, Subgroup separability of graphs of free groups with cyclic edge groups, Q. J. Math. 51 (2000) 107 MR1760573
47	D T Wise, Subgroup separability of the figure 8 knot group, Topology 45 (2006) 421 MR2218750
48	D T Wise, Morse theory, random subgraphs, and incoherent groups, Bull. Lond. Math. Soc. 43 (2011) 840 MR2854555
49	D T Wise, The structure of groups with a quasiconvex hierarchy (2012)
50	S K Yeung, Virtual first Betti number and integrality of compact complex two-ball quotients, Int. Math. Res. Not. 2004 (2004) 1967 MR2063566