Article (Scientific journals)
The maximum number of systoles for genus two Riemann surfaces with abelian differentials
Judge, Chris; Parlier, Hugo
2019In COMMENTARII MATHEMATICI HELVETICI, 94 (2), p. 399-437
Peer reviewed
 

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Keywords :
Systoles; translation surfaces; abelian differentials
Abstract :
[en] In this article, we provide bounds on systoles associated to a holomorphic 1-form omega on a Riemann surface X. In particular, we show that if X has genus two, then, up to homotopy, there are at most 10 systolic loops on (X, omega) and, moreover, that this bound is realized by a unique translation surface up to homothety. For general genus g and a holomorphic 1-form omega with one zero, we provide the optimal upper bound, 6g - 3, on the number of homotopy classes of systoles. If, in addition, X is hyperelliptic, then we prove that the optimal upper bound is 6g - 5.
Disciplines :
Mathematics
Author, co-author :
Judge, Chris;  Indiana Univ, Dept Math, Bloomington, IN 47405 USA.
Parlier, Hugo ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
External co-authors :
yes
Title :
The maximum number of systoles for genus two Riemann surfaces with abelian differentials
Publication date :
2019
Journal title :
COMMENTARII MATHEMATICI HELVETICI
ISSN :
0010-2571
Publisher :
European Mathematical Soc, Zurich, Unknown/unspecified
Volume :
94
Issue :
2
Pages :
399-437
Peer reviewed :
Peer reviewed
Funders :
Simons collaboration grant
Swiss National Science Foundation [PP00P2_153024]
Commentary :
Research partially supported by a Simons collaboration grant.; Research partially supported by Swiss National Science Foundation grant number PP00P2_153024.
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