
TL;DR
The paper provides a short proof of Kropholler's conjecture, extends Stallings' Theorem on groups with multiple ends, and generalizes the Almost Stability Theorem to inform the structure of Sageev cubings.
Contribution
It offers a concise proof of a conjecture, a relative version of Stallings' Theorem, and a generalized Almost Stability Theorem for Sageev cubings.
Findings
Proof of Kropholler's conjecture provided
Extended Stallings' Theorem to relative cases
Generalized Almost Stability Theorem for Sageev cubings
Abstract
A short proof of a conjecture of Kropholler is given. This gives a relative version of Stallings' Theorem on the structure of groups with more than one end. A generalisation of the Almost Stability Theorem is also obtained, that gives information about the structure of the Sageev cubing.
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Taxonomy
TopicsGeometric and Algebraic Topology · Advanced Operator Algebra Research · Holomorphic and Operator Theory
