The maximum number of systoles for genus two Riemann surfaces with abelian differentials release_cffor2dtdfgzbah6d4jd46dhfa

by Chris Judge, Hugo Parlier

Released as a article .

2017  

Abstract

In this article, we provide bounds on systoles associated to a holomorphic 1-form ω 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,ω) and, moreover, that this bound is realized by a unique translation surface up to homothety. For general genus g and a holomorphic 1-form ω 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.
In text/plain format

Archived Files and Locations

application/pdf  600.7 kB
file_bdgwubv4xzb3piovfjklhkw26m
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2017-03-07
Version   v2
Language   en ?
arXiv  1703.01809v2
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: 88edc61d-9f8a-4658-9a8b-559adf06b8e8
API URL: JSON