Bredon-Poincare Duality Groups

2013/11/29 by Simon St John-Green, John-Green, Simon St · 1 citation
Mathematics · #20J05 #57M07 #57P10 #Algebraic Topology (math.AT) #Algebraic structures and combinatorial models #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #math.AT #math.GR #msc:20J05 #msc:57M07 #msc:57P10

paper · pdf · doi:10.48550/arxiv.1311.7629

Revised version, added section 4.2; 27 pages, no figures

openalex publication_date 2013/11/29 · arxiv created 2014/01/08 · arxiv updated 2014/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If G is a group which admits a manifold model for BG then G is a Poincaré duality group. We study a generalisation of Poincaré duality groups, introduced initially by Davis and Leary, motivated by groups G with cocompact manifold models M for \underlineEG where M^H is a contractible submanifold for all finite subgroups H of G. We give several sources of examples and constructions of these Bredon-Poincaré duality groups, including using the equivariant reflection group trick of Davis and Leary to construct examples of Bredon-Poincaré duality groups arising from actions on manifolds M where the dimensions of the submanifolds M^H are specified. We classify Bredon-Poincaré duality groups in low dimensions, and discuss behaviour under group extensions and graphs of groups.

Citations

• On Bredon (Co-)Homological Dimensions of Groups

Cited by

• Cohomological Finiteness Properties of Groups

Related

• Some questions on subgroups of 3-dimensional Poincaré duality groups
• Equivariant Poincaré duality for cyclic groups of prime order and the Nielsen realisation problem
• Parametrised Poincaré duality and equivariant fixed points methods
• On Brown's Problem, Poincare' models for the classifying spaces for proper actions and Nielsen Realization
• On Finite domination and Poincaré duality