English

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