Duke Mathematical Journal

Families of short cycles on Riemannian surfaces

Yevgeny Liokumovich

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Abstract

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

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

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

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1454683425

Digital Object Identifier
doi:10.1215/00127094-3450208

Mathematical Reviews number (MathSciNet)
MR3498868

Zentralblatt MATH identifier
1341.53072

Subjects
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]

Keywords
Riemann surfaces systolic geometry quantitative topology width

Citation

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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