An Alexander-type duality for valuations

Adiprasito, Karim; Sanyal, Raman

doi:10.1090/S0002-9939-2014-12366-5

An Alexander-type duality for valuations
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by Karim A. Adiprasito and Raman Sanyal PDF

Proc. Amer. Math. Soc. 143 (2015), 833-843 Request permission

Abstract:

We prove an Alexander-type duality for valuations for certain subcomplexes in the boundary of polyhedra. These strengthen and simplify results of Stanley (1974) and Miller–Reiner (2005). We give a generalization of Brion’s theorem for this relative situation, and we discuss the topology of the possible subcomplexes for which the duality relation holds.

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