Path concordances as detectors of codimension-one manifold factors

TL;DR

This paper introduces the Disjoint Path Concordances Property as a key criterion to determine when the product of an ENR homology manifold with the real line is a manifold, linking it to resolvability.

Contribution

It establishes a new characterization of when X times R is a manifold based on the Disjoint Path Concordances Property for ENR homology manifolds.

Findings

X times R has the Disjoint Disks Property if and only if X has the Disjoint Path Concordances Property.

X times R is a manifold if and only if X is resolvable and has the Disjoint Path Concordances Property.

The paper provides a precise criterion for manifold recognition in product spaces involving ENR homology manifolds.

Abstract

We present a new property, the Disjoint Path Concordances Property, of an ENR homology manifold X which precisely characterizes when X times R has the Disjoint Disks Property. As a consequence, X times R is a manifold if and only if X is resolvable and it possesses this Disjoint Path Concordances Property.