%0 Generic %1 Nguyen2010 %A Nguyen, Duc-Manh %D 2010 %K imported %T On the topology of H(2) %U http://arxiv.org/abs/1003.0864 %X 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.

@misc{Nguyen2010, 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. }, added-at = {2010-03-05T08:57:48.000+0100}, author = {Nguyen, Duc-Manh}, biburl = {https://www.bibsonomy.org/bibtex/254d26acfe74e2502ea2d5ca215a458ac/uludag}, description = {On the topology of H(2)}, interhash = {f88633de997557506f88480a80ea01cc}, intrahash = {54d26acfe74e2502ea2d5ca215a458ac}, keywords = {imported}, note = {cite arxiv:1003.0864 Comment: 36 pages}, timestamp = {2010-03-05T08:57:48.000+0100}, title = {On the topology of H(2)}, url = {http://arxiv.org/abs/1003.0864}, year = 2010 }