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arXiv · 1410.8436

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 non-trivial element of the k'th homology group of the space of cycles and such that the mass of each cycle is bounded above by $C \max\{\sqrt{k}, \sqrt{g}\} \sqrt{Area(M)}$. This result is optimal up to a multiplicative constant.

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Yevgeny Liokumovich. 2014-10-30. Families of short cycles on Riemannian surfaces. https://doi.org/10.1215/00127094-3450208

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