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arXiv · 0912.3723

The dunce hat in a minimal non-extendably collapsible 3-ball

Bruno Benedetti·Frank H. Lutz
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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.

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Bruno Benedetti, Frank H. Lutz. 2013-02-01. The dunce hat in a minimal non-extendably collapsible 3-ball. https://arxiv.org/abs/0912.3723

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