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Mircea Petrache and Roger Züst
Matchings in metric spaces, the dual problem and calibrations modulo 2 view print
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| Published: |
November 8, 2016 |
| Keywords: |
Minimal matching, rectifiable chain, Kantorovich duality, calibration, tree |
| Subject: |
49Q15, 49Q20, 49Q05, 28A75 |
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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 Z2. Finally we extend the results to infinite metric spaces and present a notion of "matching dimension'' which arises naturally.
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| Acknowledgements
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.
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| Author information
Mircea Petrache:
Max-Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
decostruttivismo@gmail.com
Roger Züst:
University of Bern, Mathematical Institute, Alpeneggstrasse 22, 3012 Bern, Switzerland
roger.zuest@math.unibe.ch
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