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We investigate cohomological properties of fundamental groups of strictly developable simple complexes of groups X. We obtain a polyhedral complex equivariantly homotopy equivalent to X of the lowest possible dimension. As applications, we obtain a simple formula for proper cohomological dimension of CAT (0) groups whose actions admit a strict fundamental domain; for any building of type (W,S) that admits a chamber transitive action by a discrete group, we give a realisation of the building of the lowest possible dimension equal to the virtual cohomological dimension of W; under general assumptions, we confirm a folklore conjecture on the equality of Bredon geometric and cohomological dimensions in dimension one; finally, we give a new family of counterexamples to the strong form of Brown’s conjecture on the equality of virtual cohomological dimension and Bredon cohomological dimension for proper actions.
Petrosyan, Nansen 1 ; Prytuła, Tomasz 2
@article{10_2140_agt_2024_24_1121,
author = {Petrosyan, Nansen and Prytu{\l}a, Tomasz},
title = {Cohomological and geometric invariants of simple complexes of groups},
journal = {Algebraic and Geometric Topology},
pages = {1121--1155},
publisher = {mathdoc},
volume = {24},
number = {2},
year = {2024},
doi = {10.2140/agt.2024.24.1121},
url = {http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1121/}
}
TY - JOUR AU - Petrosyan, Nansen AU - Prytuła, Tomasz TI - Cohomological and geometric invariants of simple complexes of groups JO - Algebraic and Geometric Topology PY - 2024 SP - 1121 EP - 1155 VL - 24 IS - 2 PB - mathdoc UR - http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1121/ DO - 10.2140/agt.2024.24.1121 ID - 10_2140_agt_2024_24_1121 ER -
%0 Journal Article %A Petrosyan, Nansen %A Prytuła, Tomasz %T Cohomological and geometric invariants of simple complexes of groups %J Algebraic and Geometric Topology %D 2024 %P 1121-1155 %V 24 %N 2 %I mathdoc %U http://geodesic.mathdoc.fr/articles/10.2140/agt.2024.24.1121/ %R 10.2140/agt.2024.24.1121 %F 10_2140_agt_2024_24_1121
Petrosyan, Nansen; Prytuła, Tomasz. Cohomological and geometric invariants of simple complexes of groups. Algebraic and Geometric Topology, Tome 24 (2024) no. 2, pp. 1121-1155. doi: 10.2140/agt.2024.24.1121
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