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math.GT2012
Smoothing discrete Morse theory
Bruno Benedetti
After surveying classical notions of PL topology of the Seventies, we clarify the relation between Morse theory and its discretization by Forman. We show that PL handles theory and…
math.CO2012
Subdivisions, shellability, and collapsibility of products
Karim Alexander Adiprasito, Bruno Benedetti
We prove that the second derived subdivision of any rectilinear triangulation of any convex polytope is shellable. Also, we prove that the first derived subdivision of every rectil…
math.GT2012
Tight complexes in 3-space admit perfect discrete Morse functions
Karim Adiprasito, Bruno Benedetti
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 a…