Detecting codimension one manifold factors with topographical techniques

TL;DR

This paper develops topographical techniques and introduces three ribbons properties to recognize when a space times a line is a manifold, advancing understanding of codimension one manifold factors in higher dimensions.

Contribution

It formalizes topographical methods and introduces three new ribbons properties to identify codimension one manifold factors in higher-dimensional spaces.

Findings

Proves recognition theorems for codimension one manifold factors.

Introduces crinkled, twisted crinkled, and fuzzy ribbons properties.

Shows conditions under which $X imes \\mathbb{R}$ is a manifold.

Abstract

We prove recognition theorems for codimension one manifold factors of dimension $n \geq 4$. 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 $n \geq 3$ 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.