The space consists of pairs , where is a Riemann surface of genus two, and is a holomorphic 1-form which has only one zero of order two. There exists a natural action of on by multiplication to the holomorphic 1-form. In this paper, we single out a proper subgroup of generated by three elements, and show that the space can be identified with the quotient , where is the Jacobian locus in the Siegel upper half space . A direct consequence of this result is that . The group can also be interpreted as the image of the fundamental group of in the symplectic group .
Cite this article
Duc-Manh Nguyen, On the topology of . Groups Geom. Dyn. 8 (2014), no. 2, pp. 513–551DOI 10.4171/GGD/237