On the topology of H(2)
Geometric Topology
2012-03-09 v2 Differential Geometry
Abstract
In this paper, we first single out a proper subgroup \Gamma of Sp(4,Z) generated by three elements, which arises from the parallelogram decompositions of translation surfaces in H(2). We then prove that the space H(2)/C* can be identified to the quotient J_2/\Gamma, where J_2 is the Jacobian locus in the Siegel upper half space H_2, in other words, the group \Gamma is the image in Sp(4,Z) of the fundamental group of the space H(2)/C*. A direct consequence of this fact is that [Sp(4,Z):\Gamma]=6.
Keywords
Cite
@article{arxiv.1003.0864,
title = {On the topology of H(2)},
author = {Duc-Manh Nguyen},
journal= {arXiv preprint arXiv:1003.0864},
year = {2012}
}
Comments
34 pages, 17 figures