Reference : The maximum number of systoles for genus two Riemann surfaces with abelian differentials
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/30056
The maximum number of systoles for genus two Riemann surfaces with abelian differentials
English
Judge, Chris [> >]
Parlier, Hugo mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
1-Mar-2017
Yes
[en] Mathematics - Geometric Topology ; Mathematics - Differential Geometry
[en] This article explores the length and number of systoles associated to holomorphic $1$-forms on surfaces. In particular, we show that up to homotopy, there are at most $10$ systolic loops on such a genus two surface and that the bound is realized by a unique translation surface up to homothety. We also provide sharp upper bounds on the the number of homotopy classes of systoles for a holomorphic $1$-form with a single zero in terms of the genus.
http://hdl.handle.net/10993/30056
http://esoads.eso.org/abs/2017arXiv170301809J
37 pages, 17 figure. Fixed a figure, a statement and added a reference
https://arxiv.org/abs/1703.01809

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