Matchings in metric spaces, the dual problem and calibrations modulo 2
Metric Geometry
2016-09-22 v2 Combinatorics
Differential Geometry
Optimization and Control
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 . Finally we extend the results to infinite metric spaces and present a notion of "matching dimension" which arises naturally.
Keywords
Cite
@article{arxiv.1410.0062,
title = {Matchings in metric spaces, the dual problem and calibrations modulo 2},
author = {Mircea Petrache and Roger Züst},
journal= {arXiv preprint arXiv:1410.0062},
year = {2016}
}
Comments
We corrected some typos and clarified some of the notations and formulations. The new version uses the New York Journal of Mathematics template