32 citations · 122 across the 43 of their papers we have counts for
4 papers · 1 filter
Many projectively unique polytopes
Karim A. Adiprasito, Günter M. Ziegler
We construct an infinite family of 4-polytopes whose realization spaces have dimension smaller or equal to 96. This in particular settles a problem going back to Legendre and Stein…
Combinatorial stratifications and minimality of 2-arrangements
Karim A. Adiprasito
We prove that the complement of any affine 2-arrangement in R^d is minimal, that is, it is homotopy equivalent to a cell complex with as many i-cells as its i-th rational Betti num…
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…
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…