Tight complexes in 3-space admit perfect discrete Morse functions

Karim Adiprasito; Bruno Benedetti

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arXiv · 1202.3390

Tight complexes in 3-space admit perfect discrete Morse functions

Karim Adiprasito·Bruno Benedetti

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Abstract

In 1967, Chillingworth proved that all convex simplicial 3-balls are collapsible. Using the classical notion of tightness, we generalize this to arbitrary manifolds: We show that all tight simplicial 3-manifolds admit some perfect discrete Morse function. We also strengthen Chillingworth's theorem by proving that all convex simplicial 3-balls are non-evasive. In contrast, we show that many non-evasive 3-balls are not convex.

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Karim Adiprasito, Bruno Benedetti. 2012-04-07. Tight complexes in 3-space admit perfect discrete Morse functions. https://arxiv.org/abs/1202.3390

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