How different can h-cobordant manifolds be?

TL;DR

This paper explores the diversity of manifolds that are h-cobordant to a given manifold, clarifying previous claims and examining the implications for special manifolds like lens spaces.

Contribution

It provides a detailed analysis of the homeomorphism types of h-cobordant manifolds, especially focusing on special manifolds such as lens spaces, and clarifies earlier misconceptions.

Findings

Clarified the range of homeomorphism types within h-cobordisms.

Revisited and clarified claims about h-cobordisms of special manifolds.

Enhanced understanding of the structure of h-cobordant manifolds.

Abstract

We study the homeomorphism types of manifolds h-cobordant to a fixed one. Our investigation is partly motivated by the notion of special manifolds introduced by Milnor in his study of lens spaces. In particular we revisit and clarify some of the claims concerning h-cobordisms of these manifolds.