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Abstract: R. Stanley proved a strong estimate on the number of faces of a centrally symmetric simple (i.e. co-simplicial) polytope. This results may be reformulated in terms of an estimate on the cohomology of a quasi-smooth toric variety which possesses an involution. We extend the later estimate to arbitrary symplectic manifolds endowed with a Hamiltonian torus action and an involution compatible with this action (in a certain sense). In particular, we obtain a new, simpler proof of Stanley's theorem.
Using results of Bernstein and Lunts, we extend our method to a study of singular toric varieties with involution. This leads to an estimate on the intersection cohomology of such a variety similar to the estimate obtained by Stanley in a quasi-smooth case. In particular, we show that Stanley's estimate on the number of faces remains true for any rational (not necessarily simple) centrally-symmetric polytope. |
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| Web page: Alexandru I. Suciu | Created: Jan. 21, 1999 Updated: Feb. 11, 1999 |
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URL: http://www.math.neu.edu/~suciu/gas/braverman.html |