Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

TL;DR

This paper demonstrates that finite-dimensional resolvable generalized manifolds possessing the piecewise disjoint arc-disk property are indeed codimension one manifold factors, and explores related properties and their implications.

Contribution

It establishes a link between the piecewise disjoint arc-disk property and being a codimension one manifold factor, expanding understanding of general position properties.

Findings

All finite-dimensional resolvable generalized manifolds with the property are codimension one manifold factors.

The piecewise disjoint arc-disk property relates closely to other general position properties.

Known examples of codimension one manifold factors satisfy the property.

Abstract

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension $n\geq 4$ determined by general position properties, the piecewise disjoint arc-disk property is satisfied.