Toric cohomological rigidity of simple convex polytopes

Details Toric cohomological rigidity of simple convex polytopes Toric cohomological rigidity of simple convex polytopes

2008-07-30

arxiv.org/abs/0807.4800v2

Journal of the London Math. Society, II Ser. 82 (2010), no.2, 343-360

Mathematics

Algebraic Topology

18 pages, 1 figure, 2 tables; revised version

Scientific paper

A simple convex polytope $P$ is \emph{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 article we investigate the cohomological rigidity of polytopes and establish it for several new classes of polytopes including products of simplices. Cohomological rigidity of $P$ is related to the \emph{bigraded Betti numbers} of its \emph{Stanley--Reisner ring}, another important invariants coming from combinatorial commutative algebra.

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