Tight complexes in 3-space admit perfect discrete Morse functions
Geometric Topology
2012-04-10 v2 Combinatorics
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 simplicial 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 are not convex.
Keywords
Cite
@article{arxiv.1202.3390,
title = {Tight complexes in 3-space admit perfect discrete Morse functions},
author = {Karim Adiprasito and Bruno Benedetti},
journal= {arXiv preprint arXiv:1202.3390},
year = {2012}
}
Comments
13 pages, 4 figures, some typos corrected