TL;DR
This paper discusses the Kropholler Conjecture, providing insights into its proof, the challenges faced, and potential approaches for establishing a correct proof, contributing to the understanding of group ends and related conjectures.
Contribution
It offers a detailed analysis of the proof attempts for the Kropholler Conjecture and explores avenues for a valid proof, clarifying previous inaccuracies.
Findings
Initial proof was incorrect
Second proof was still inadequate
Identifies difficulties and potential solutions
Abstract
The first version of this paper gave another proof of the Kropholler Conjecture, which gives a relative version of Stallings Ends Theorem, following an earlier incorrect proof. It has been pointed out by Sam Shepherd that the the second proof was still inadequate. We explain the difficulty and possible ways to obtain a correct proof.
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Taxonomy
TopicsComputational Geometry and Mesh Generation · Computability, Logic, AI Algorithms · Data Visualization and Analytics