The maximum number of systoles for genus two Riemann surfaces with abelian differentials

Reference : The maximum number of systoles for genus two Riemann surfaces with abelian differentials


	Document type :	E-prints/Working papers : Already available on another site
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics
	To cite this reference:	http://hdl.handle.net/10993/30056

Title :	The maximum number of systoles for genus two Riemann surfaces with abelian differentials
Language :	English
Author, co-author :	Judge, Chris [> >]
	Parlier, Hugo [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit]
Publication date :	1-Mar-2017
Peer reviewed :	Yes
Keywords :	[en] Mathematics - Geometric Topology ; Mathematics - Differential Geometry
Abstract :	[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.
Permalink :	http://hdl.handle.net/10993/30056
Other URL :	http://esoads.eso.org/abs/2017arXiv170301809J
Commentary :	37 pages, 17 figure. Fixed a figure, a statement and added a reference
source URL :	https://arxiv.org/abs/1703.01809

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