Centralisers in Houghton's Groups
Simon St John-Green
TL;DR
This paper investigates the structure of centralisers within Houghton's groups, examining their properties and finiteness conditions related to cohomology and subgroup classifications.
Contribution
It provides a detailed analysis of centralisers and explores Bredon (co-)homological finiteness conditions in Houghton's groups, advancing understanding of their algebraic and homological properties.
Findings
Characterization of centralisers of elements and subgroups in Houghton's groups
Identification of Bredon (co-)homological finiteness properties
Analysis of Bredon-FPn conditions in the context of Houghton's groups
Abstract
We study the centralisers of elements, finite subgroups and virtually cyclic subgroups of Houghton's group Hn. We discuss various Bredon (co-)homological finiteness conditions satisfied by Hn including the Bredon (co-)homological dimension and Bredon-FPn conditions, which are analogs of the ordinary co-homological dimension and FPn conditions respectively.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Geometric and Algebraic Topology