[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.
Disciplines :
Mathematics
Author, co-author :
Judge, Chris
Parlier, Hugo ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Language :
English
Title :
The maximum number of systoles for genus two Riemann surfaces with abelian differentials