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arXiv · 1410.0062

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

Mircea Petrache·Roger Züst
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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.

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Mircea Petrache, Roger Züst. 2014-09-30. Matchings in metric spaces, the dual problem and calibrations modulo 2. https://arxiv.org/abs/1410.0062

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