Tight complexes in 3-space admit perfect discrete Morse functions

Karim Adiprasito, Bruno Benedetti

Research output: Contribution to journalArticle

2 Citations (Scopus)

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 polytopal 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 cannot be realized in a convex way.

Original languageEnglish (US)
Pages (from-to)71-84
Number of pages14
JournalEuropean Journal of Combinatorics
Volume45
DOIs
StatePublished - Apr 1 2015
Externally publishedYes

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Morse Function
Ball
Tightness
Generalise
Arbitrary
Theorem

ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

Cite this

Tight complexes in 3-space admit perfect discrete Morse functions. / Adiprasito, Karim; Benedetti, Bruno.

In: European Journal of Combinatorics, Vol. 45, 01.04.2015, p. 71-84.

Research output: Contribution to journalArticle

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