TY - JOUR
T1 - Tight complexes in 3-space admit perfect discrete Morse functions
AU - Adiprasito, Karim
AU - Benedetti, Bruno
N1 - Publisher Copyright:
© 2014 Elsevier Ltd.
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
U2 - 10.1016/j.ejc.2014.10.002
DO - 10.1016/j.ejc.2014.10.002
M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???
AN - SCOPUS:84909979746
SN - 0195-6698
VL - 45
SP - 71
EP - 84
JO - European Journal of Combinatorics
JF - European Journal of Combinatorics
ER -