The homology systole of hyperbolic Riemann surfaces

Details The homology systole of hyperbolic Riemann surfaces The homology systole of hyperbolic Riemann surfaces

2010-10-02

arxiv.org/abs/1010.0358v2

Mathematics

Geometric Topology

7 pages, 5 figures

Scientific paper

The main goal of this note is to show that the study of closed hyperbolic
surfaces with maximum length systole is in fact the study of surfaces with
maximum length homological systole. The same result is shown to be true for
once-punctured surfaces, and is shown to fail for surfaces with a large number
of cusps.

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