Matchings in metric spaces, the dual problem and calibrations modulo 2

2014/09/30 by Petrache, Mircea, Züst, Roger
#05C05 #28A75 #49Q15 #49Q20 #58A10 #58A25 #Combinatorics (math.CO) #Differential Geometry (math.DG) #FOS: Mathematics #Metric Geometry (math.MG) #Optimization and Control (math.OC)

paper · doi:10.48550/arxiv.1410.0062

Abstract

We show that for a metric space with an even number of points there is a 1-Lipschitz map to a tree-like space with the same matching number. This result gives the first basic version of an unoriented Kantorovich duality. The study of the duality gives a version of global calibrations for 1-chains with coefficients in \mathbb Z₂. Finally we extend the results to infinite metric spaces and present a notion of "matching dimension" which arises naturally.

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