@article{d494e5daf18c4d7b825533567ab1ff68,
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 = "Funding Information: The authors would like to thank Frank Lutz, G{\"u}nter Ziegler and Igor Pak for useful suggestions and references. The first author was supported by an EPDI/IPDE postdoctoral fellowship and a Minerva Fellowship of the Max Planck Society . The second author was supported by the DFG Collaborative . Research Center TRR , 109 , “Discretization in Geometry and Dynamics”, the G{\"o}ran Gustafsson Foundation , and the Swedish Research Council (Vetenskapsr{\aa}det) via the grant “Triangulerade M{\aa}ngfalder, Knutteori i diskrete Morseteori”.",
year = "2015",
month = apr,
day = "1",
doi = "10.1016/j.ejc.2014.10.002",
language = "English (US)",
volume = "45",
pages = "71--84",
journal = "European Journal of Combinatorics",
issn = "0195-6698",
publisher = "Academic Press Inc.",
}