Toric cohomological rigidity of simple convex polytopes
By Suyoung Choi, T. Panov, D. Suh. 2008
49 citations recorded by the source corpus.
A simple convex polytope P is cohomologically rigid if its combinatorial structure is determined by the cohomology ring of a quasitoric manifold over P. Not every P has this property, but some important polytopes such as simplices or cubes are known to be cohomologically rigid. In this paper we investigate the cohomological rigidity of polytopes and establish it for several new classes of polytopes, including products of simplices. The cohomological rigidity of P is related to the bigraded Betti numbers of its Stanley–Reisner ring, another important invariant coming from combinatorial commutative algebra.
Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Discrete Mathematics and Combinatorics
View Paper: https://www.semanticscholar.org/paper/787bb44f2dcb6581bb3fa3d2bac34d9b8da31572
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In Algebra and Number Theory
In Computational Theory and Mathematics
In Discrete Mathematics and Combinatorics
Citations in the corpus
- Topological classification of generalized Bott towers (2008, background): “Similarly to Remark 1.2 the assumption “over a product of simplices” in the corollary above can be dropped by a result in [2].”
- Toric topology (2012, background): “From this viewpoint, Choi-Panov-Suh[14] discusses an analogous rigidity problem for simple convex polytopes.”