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 (US) |
|---|---|
| Pages (from-to) | 71-84 |
| Number of pages | 14 |
| Journal | European Journal of Combinatorics |
| Volume | 45 |
| DOIs | |
| State | Published - Apr 1 2015 |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - Tight complexes in 3-space admit perfect discrete Morse functions
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.
UR - http://www.scopus.com/inward/record.url?scp=84909979746&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=84909979746&partnerID=8YFLogxK
U2 - 10.1016/j.ejc.2014.10.002
DO - 10.1016/j.ejc.2014.10.002
M3 - Article
VL - 45
SP - 71
EP - 84
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
SN - 0195-6698
ER -