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

• Autores: José Agapito, Leonor Godinho
• Localización: Advances in mathematics, ISSN 0001-8708, Vol. 214, Nº 1, 2007, págs. 379-416
• Idioma: inglés
• DOI: 10.1016/j.aim.2007.02.008
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• Resumen

  • 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.