New polytope decompositions and Euler-Maclaurin formulas for simple integral polytopes

  • Agapito J
  • Godinho L
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Abstract

We give new weighted decompositions for simple polytopes, generalizing previous results of Lawrence-Varchenko and Brianchon-Gram. We start with Witten's non-abelian localization principle in equivariant cohomology for the norm-square of the moment map in the context of toric varieties to obtain a decomposition for Delzant polytopes. Then, by a purely combinatorial argument, we show that this formula holds for any simple polytope. As an application, we study Euler-Maclaurin formulas. © 2007 Elsevier Inc. All rights reserved.

Author-supplied keywords

  • Euler-Maclaurin formula
  • Localization in equivariant cohomology
  • Polytope decompositions

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Authors

  • José Agapito

  • Leonor Godinho

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