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

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 ${\mathbb{Z}}_2$. Finally we extend the results to infinite metric spaces and present a notion of "matching dimension" which arises naturally.

We corrected some typos and clarified some of the notations and formulations. The new version uses the New York Journal of Mathematics template

References in corpus (2)

• Lemma Poincaré for L_infty,loc - forms
• Some results on maps that factor through a tree