New York Journal of Mathematics
Volume 22 (2016) 1283-1318


Mircea Petrache and Roger Züst

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

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Published: November 8, 2016
Keywords: Minimal matching, rectifiable chain, Kantorovich duality, calibration, tree
Subject: 49Q15, 49Q20, 49Q05, 28A75

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 Z2. Finally we extend the results to infinite metric spaces and present a notion of "matching dimension'' which arises naturally.


The first author was supported by the Fondation des Sciences Mathématiques de Paris and the second author was supported by the Swiss National Science Foundation.

Author information

Mircea Petrache:
Max-Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany

Roger Züst:
University of Bern, Mathematical Institute, Alpeneggstrasse 22, 3012 Bern, Switzerland