On the topology of $H(2)$

Duc-Manh Nguyen (1)

1 Équipe Géométrie

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.

Domaines: Topologie géométrique [math.GT]; Géométrie différentielle [math.DG]

Duc-Manh Nguyen. On the topology of $H(2)$. Groups, Geometry, and Dynamics, 2014, 8 (2014) (2), pp.513-551. ⟨10.4171/GGD/236⟩. ⟨hal-00974004⟩