The dunce hat in a minimal non-extendably collapsible 3-ball
Algebraic Topology
2013-02-04 v2 Combinatorics
Metric Geometry
Abstract
We obtain a geometric realization of a minimal 8-vertex triangulation of the dunce hat in Euclidean 3-space. We show there is a simplicial 3-ball with 8 vertices that is collapsible, but also collapses onto the dunce hat, which is not collapsible. This 3-ball is as small as possible, because all triangulated 3-balls with fewer vertices are extendably collapsible. As we will see, the Alexander dual of the dunce hat is collapsible.
Keywords
Cite
@article{arxiv.0912.3723,
title = {The dunce hat in a minimal non-extendably collapsible 3-ball},
author = {Bruno Benedetti and Frank H. Lutz},
journal= {arXiv preprint arXiv:0912.3723},
year = {2013}
}
Comments
6 pages, 7 figures, Electronic Geometry Models, to appear