Detecting codimension one manifold factors with topographical techniques

Abstract

We prove recognition theorems for codimension one manifold factors of dimension $n\ge 4$. In particular, we formalize topographical methods and introduce three ribbons properties: the crinkled ribbons property, the twisted crinkled ribbons property, and the fuzzy ribbons property. We show that $X\times \mathbb{R}$ is a manifold in the cases when $X$ is a resolvable generalized manifold of finite dimension $n\ge 3$ with either: (1) the crinkled ribbons property; (2) the twisted crinkled ribbons property and the disjoint point disk property; or (3) the fuzzy ribbons property.

References in corpus (2)

• The Bing-Borsuk and the Busemann Conjectures
• Path concordances as detectors of codimension-one manifold factors

Cited by in corpus (1)

• The Bing-Borsuk and the Busemann Conjectures