Duke Mathematical Journal

Families of short cycles on Riemannian surfaces

Yevgeny Liokumovich

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Let M be a closed Riemannian surface of genus g. We construct a family of 1-cycles on M that represents a nontrivial element of the kth homology group of the space of cycles and such that the mass of each cycle is bounded above by Cmax {k,g}Area(M). This result is optimal up to a multiplicative constant.

Article information

Duke Math. J., Volume 165, Number 7 (2016), 1363-1379.

Received: 15 November 2014
Revised: 16 August 2015
First available in Project Euclid: 5 February 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 53C23: Global geometric and topological methods (à la Gromov); differential geometric analysis on metric spaces
Secondary: 30F10: Compact Riemann surfaces and uniformization [See also 14H15, 32G15]

Riemann surfaces systolic geometry quantitative topology width


Liokumovich, Yevgeny. Families of short cycles on Riemannian surfaces. Duke Math. J. 165 (2016), no. 7, 1363--1379. doi:10.1215/00127094-3450208. https://projecteuclid.org/euclid.dmj/1454683425

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