Tight complexes in 3-space admit perfect discrete Morse functions

Karim Adiprasito, Bruno Benedetti

Research output: Contribution to journalArticle

3 Scopus citations


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
StatePublished - Apr 1 2015
Externally publishedYes


ASJC Scopus subject areas

  • Discrete Mathematics and Combinatorics

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