At most 27 length inequalities define Maskit's fundamental domain for the modular group in genus 2
Abstract
In recently published work Maskit constructs a fundamental domain D_g for the Teichmueller modular group of a closed surface S of genus g>1. Maskit's technique is to demand that a certain set of 2g non-dividing geodesics C_{2g} on S satisfies certain shortness criteria. This gives an a priori infinite set of length inequalities that the geodesics in C_{2g} must satisfy. Maskit shows that this set of inequalities is finite and that for genus g=2 there are at most 45. In this paper we improve this number to 27. Each of these inequalities: compares distances between Weierstrass points in the fundamental domain S-C_4 for S; and is realised (as an equality) on one or other of two special surfaces.
Keywords
Cite
@article{arxiv.math/9811180,
title = {At most 27 length inequalities define Maskit's fundamental domain for the modular group in genus 2},
author = {David Griffiths},
journal= {arXiv preprint arXiv:math/9811180},
year = {2016}
}
Comments
14 pages. Published copy, also available at http://www.maths.warwick.ac.uk/gt/GTMon1/paper9.abs.html