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Relative ends and splittings of groups

Relative ends and splittings of groups
Relative ends and splittings of groups
This thesis is motivated by a long-standing conjecture on groups with Bredon cohomological dimension one and their action on trees with stabilisers in a specific family of subgroups. Chapter 1 consists of the first approach to deal with the problem following steps of known results for families of finite and virtually cyclic subgroups. As a consequent of this attempt, we answer a question on the Bredon cohomological and geometric dimension of free abelian groups with finite rank.

The Main Theorem in Chapter 2 provides a partial answer to Kropholler’s Conjecture on splittings of groups, which has been thought to be an alternative step for the proof of the conjecture stated in Chapter 1. We define the notion of relative ends, commensurable subgroups, almost invariant sets and the relation between those and splittings of groups, or equivalently, actions on trees with special stabilisers.
University of Southampton
Lopes Onorio, Ana Claudia
23344670-6064-465d-88cb-1f70b37933f6
Lopes Onorio, Ana Claudia
23344670-6064-465d-88cb-1f70b37933f6
Petrosyan, Nansen
f169cfd6-aeee-4ad2-b147-0bf77dd1f9b6

Lopes Onorio, Ana Claudia (2018) Relative ends and splittings of groups. University of Southampton, Doctoral Thesis, 83pp.

Record type: Thesis (Doctoral)

Abstract

This thesis is motivated by a long-standing conjecture on groups with Bredon cohomological dimension one and their action on trees with stabilisers in a specific family of subgroups. Chapter 1 consists of the first approach to deal with the problem following steps of known results for families of finite and virtually cyclic subgroups. As a consequent of this attempt, we answer a question on the Bredon cohomological and geometric dimension of free abelian groups with finite rank.

The Main Theorem in Chapter 2 provides a partial answer to Kropholler’s Conjecture on splittings of groups, which has been thought to be an alternative step for the proof of the conjecture stated in Chapter 1. We define the notion of relative ends, commensurable subgroups, almost invariant sets and the relation between those and splittings of groups, or equivalently, actions on trees with special stabilisers.

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Lopes Onorio, Ana Claudia - Version of Record
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Published date: August 2018

Identifiers

Local EPrints ID: 428055
URI: https://eprints.soton.ac.uk/id/eprint/428055
PURE UUID: 33aecc27-0b03-4569-9124-f273112c6bea

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Date deposited: 07 Feb 2019 17:30
Last modified: 13 Mar 2019 17:36

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