Toric cohomological rigidity of simple convex polytopes
Abstract
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{StanleyReisner ring}, another important invariants coming from combinatorial commutative algebra.
 Publication:

arXiv eprints
 Pub Date:
 July 2008
 DOI:
 10.48550/arXiv.0807.4800
 arXiv:
 arXiv:0807.4800
 Bibcode:
 2008arXiv0807.4800C
 Keywords:

 Mathematics  Algebraic Topology;
 Mathematics  Combinatorics;
 55Nxx;
 52Bxx
 EPrint:
 18 pages, 1 figure, 2 tables