Tight complexes in 3-space admit perfect discrete Morse functions

Karim Adiprasito; Bruno Benedetti

doi:10.1016/j.ejc.2014.10.002

Tight complexes in 3-space admit perfect discrete Morse functions

Research output: Contribution to journal › Article › peer-review

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 language	English
Pages (from-to)	71-84
Number of pages	14
Journal	European Journal of Combinatorics
Volume	45
DOIs	https://doi.org/10.1016/j.ejc.2014.10.002
State	Published - 1 Apr 2015
Externally published	Yes

All Science Journal Classification (ASJC) codes

Discrete Mathematics and Combinatorics

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10.1016/j.ejc.2014.10.002

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title = "Tight complexes in 3-space admit perfect discrete Morse functions",

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.",

author = "Karim Adiprasito and Bruno Benedetti",

note = "Publisher Copyright: {\textcopyright} 2014 Elsevier Ltd.",

year = "2015",

month = apr,

day = "1",

doi = "10.1016/j.ejc.2014.10.002",

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AU - Adiprasito, Karim

AU - Benedetti, Bruno

PY - 2015/4/1

Y1 - 2015/4/1

N2 - 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.

AB - 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.

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U2 - 10.1016/j.ejc.2014.10.002

DO - 10.1016/j.ejc.2014.10.002

M3 - مقالة

SN - 0195-6698

VL - 45

SP - 71

EP - 84

JO - European Journal of Combinatorics

JF - European Journal of Combinatorics

ER -

Tight complexes in 3-space admit perfect discrete Morse functions

Abstract

All Science Journal Classification (ASJC) codes

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