English

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

Geometric Topology 2013-09-10 v1 Differential Geometry

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 n4n\geq 4 determined by general position properties, the piecewise disjoint arc-disk property is satisfied.

Keywords

Cite

@article{arxiv.1309.1866,
  title  = {Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties},
  author = {Denise M. Halverson and Dušan Repovš},
  journal= {arXiv preprint arXiv:1309.1866},
  year   = {2013}
}