A Manual for Ends, Semistability and Simple Connectivity at Infinity for Groups and Spaces
Michael Mihalik

TL;DR
This paper provides a comprehensive, updated overview of the current understanding of ends, semistability, and simple connectivity at infinity for groups and spaces, including new results and historical context.
Contribution
It compiles and discusses the latest results on these topological properties, introduces new findings, and offers a detailed index to aid researchers in the field.
Findings
Updated results on semistability and simple connectivity at infinity
New insights into the second cohomology of groups
Inclusion of mapping class groups and new indices
Abstract
This -edition article is intended to be an up-to-date archive of the current state of the questions: Which finitely generated groups : have semistable fundamental group at infinity; are simply connected at infinity; are such that is free abelian or trivial. The idea is not to reprove these results, but to provide a historical record of the progress on these questions and provide a list of the most general results. We also prove or cite all of the results that make up the basic theory. The first Chapter is devoted to ends of groups and spaces, and the second to semistability at infinity, simple connectivity at infinity and second cohomology of groups. Definitions, basic facts and lists of general results are given in each Chapter. A number of results proven here are new and a number of authors have contributed results. We end with an Index for simply…
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Taxonomy
Topicsadvanced mathematical theories · Mathematical and Theoretical Analysis · Algebraic and Geometric Analysis
