Algebraic & Geometric Topology Volume 24, issue 2 (2024)

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

Submission form

Editorial board

Subscriptions

ISSN (electronic): 1472-2739

ISSN (print): 1472-2747

Author index

To appear

Other MSP journals

Cohomological and geometric invariants of simple complexes of groups

Nansen Petrosyan and Tomasz Prytuła

Algebraic & Geometric Topology 24 (2024) 1121–1155

DOI: 10.2140/agt.2024.24.1121

Bibliography

1	M Aschbacher, Y Segev, A fixed point theorem for groups acting on finite 2–dimensional acyclic simplicial complexes, Proc. Lond. Math. Soc. 67 (1993) 329 MR1226605
2	A Ash, Deformation retracts with lowest possible dimension of arithmetic quotients of self-adjoint homogeneous cones, Math. Ann. 225 (1977) 69 MR427490
3	P Baum, A Connes, N Higson, Classifying space for proper actions and K–theory of group C^∗–algebras, from: "C^∗–algebras : 1943–1993" (editor R S Doran), Contemp. Math. 167, Amer. Math. Soc. (1994) 240 MR1292018
4	M Bestvina, The virtual cohomological dimension of Coxeter groups, from: "Geometric group theory, I" (editors G A Niblo, M A Roller), Lond. Math. Soc. Lect. Note Ser. 181, Cambridge Univ. Press (1993) 19 MR1238512
5	M R Bridson, A Haefliger, Metric spaces of non-positive curvature, 319, Springer (1999) MR1744486
6	K S Brown, Groups of virtually finite dimension, from: "Homological group theory" (editor C T C Wall), Lond. Math. Soc. Lect. Note Ser. 36, Cambridge Univ. Press (1979) 27 MR0564419
7	K S Brown, Cohomology of groups, 87, Springer (1982) MR0672956
8	M W Davis, Buildings are CAT(0), from: "Geometry and cohomology in group theory" (editors P H Kropholler, G A Niblo, R Stöhr), Lond. Math. Soc. Lect. Note Ser. 252, Cambridge Univ. Press (1998) 108 MR1709955
9	M W Davis, The geometry and topology of Coxeter groups, 32, Princeton Univ. Press (2008) MR2360474
10	M W Davis, T Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62 (1991) 417 MR1104531
11	D Degrijse, A cohomological characterization of locally virtually cyclic groups, Adv. Math. 305 (2017) 935 MR3570151
12	D Degrijse, C Martínez-Pérez, Dimension invariants for groups admitting a cocompact model for proper actions, J. Reine Angew. Math. 721 (2016) 233 MR3574882
13	F Dembegioti, N Petrosyan, O Talelli, Intermediaries in Bredon (co)homology and classifying spaces, Publ. Mat. 56 (2012) 393 MR2978329
14	W Dicks, M J Dunwoody, Groups acting on graphs, 17, Cambridge Univ. Press (1989) MR1001965
15	A N Dranishnikov, On the virtual cohomological dimensions of Coxeter groups, Proc. Amer. Math. Soc. 125 (1997) 1885 MR1422863
16	M J Dunwoody, Accessibility and groups of cohomological dimension one, Proc. Lond. Math. Soc. 38 (1979) 193 MR531159
17	M Fuentes, The equivariant K– and KO–theory of certain classifying spaces via an equivariant Atiyah–Hirzebruch spectral sequence, preprint (2019) arXiv:1905.02972
18	J L Harer, The virtual cohomological dimension of the mapping class group of an orientable surface, Invent. Math. 84 (1986) 157 MR830043
19	J Harlander, On the dimension of groups acting on buildings, from: "Groups St Andrews 1997 in Bath, I" (editors C M Campbell, E F Robertson, N Ruskuc, G C Smith), Lond. Math. Soc. Lect. Note Ser. 260, Cambridge Univ. Press (1999) 318 MR1676627
20	J Harlander, H Meinert, Higher generation subgroup sets and the virtual cohomological dimension of graph products of finite groups, J. Lond. Math. Soc. 53 (1996) 99 MR1362689
21	I J Leary, B E A Nucinkis, Some groups of type V F, Invent. Math. 151 (2003) 135 MR1943744
22	I J Leary, N Petrosyan, On dimensions of groups with cocompact classifying spaces for proper actions, Adv. Math. 311 (2017) 730 MR3628229
23	W Lück, Survey on classifying spaces for families of subgroups, from: "Infinite groups: geometric, combinatorial and dynamical aspects", Progr. Math. 248, Birkhäuser (2005) 269 MR2195456
24	C Martínez-Pérez, Euler classes and Bredon cohomology for groups with restricted families of finite subgroups, Math. Z. 275 (2013) 761 MR3127036
25	C Martínez-Pérez, B E A Nucinkis, Bredon cohomological finiteness conditions for generalisations of Thompson groups, Groups Geom. Dyn. 7 (2013) 931 MR3134031
26	N Petrosyan, T Prytuła, Bestvina complex for group actions with a strict fundamental domain, Groups Geom. Dyn. 14 (2020) 1277 MR4186475
27	K Vogtmann, Automorphisms of free groups and outer space, Geom. Dedicata 94 (2002) 1 MR1950871