Shellability and Sphericity of the quasi-arc complex of the Möbius strip

Jon Wilson

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arXiv · 1510.05419

Shellability and Sphericity of the quasi-arc complex of the Möbius strip

Jon Wilson

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Abstract

Shellability of a simplicial complex has many useful structural implications. In particular, it was shown by Danaraj and Klee that every shellable pseudo-manifold is a PL-sphere. The purpose of this paper is to prove the shellability of the quasi-arc complex of the Möbius strip. Along the way we provide elementary proofs of the shellability of the arc complex of the $n$-gon and the cylinder. In turn, applying the result of Danaraj and Klee, we obtain the sphericity of all of these complexes.

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Jon Wilson. 2015-10-19. Shellability and Sphericity of the quasi-arc complex of the Möbius strip. https://arxiv.org/abs/1510.05419

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