The integral polytope group

2016/05/04 by Funke, Florian · 3 citations
#FOS: Mathematics #Geometric Topology (math.GT) #Group Theory (math.GR) #Metric Geometry (math.MG)

paper · doi:10.48550/arxiv.1605.01217

Abstract

We show that the Grothendieck group associated to integral polytopes in ℝⁿ is free-abelian by providing an explicit basis. Moreover, we identify the involution on this polytope group given by reflection about the origin as a sum of Euler characteristic type. We also compute the kernel of the norm map sending a polytope to its induced seminorm on the dual of ℝⁿ.

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• Signed Minkowski decompositions of convex polygons into minimum simplices and factorization of max-plus functions

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