Fundamental groups, homology equivalences and one-sided h-cobordisms

TL;DR

This paper establishes conditions under which a map between manifolds induces homology equivalences and classifies one-sided h-cobordisms using Quillen's plus construction and Whitehead torsions.

Contribution

It provides a necessary and sufficient condition for fundamental group homomorphisms to induce homology equivalences and classifies one-sided h-cobordisms up to diffeomorphism.

Findings

Characterization of when a fundamental group homomorphism induces a homology equivalence

Classification of one-sided h-cobordisms using Quillen's plus construction

Application of Whitehead torsions in the classification process

Abstract

We give a sufficient and necessary condition of the fundamental group homomorphism of a map between manifolds to induce homology equivalences. Moreover, a classification of one-sided h-cobordism of manifolds up to diffeomorphisms is obtained, based on Quillen's plus construction with Whitehead torsions.