Prym Representations of Mapping Class Groups
- Cite this article as:
- Looijenga, E. Geometriae Dedicata (1997) 64: 69. doi:10.1023/A:1004909416648
- 165 Downloads
Let S be a closed orientable surface of genus at least 2 and let \(\widetilde S\) to S be a connected finite abelian covering with covering group $G$. The lifts of liftable mapping classes of S determine a central extension (by G) of a subgroup of finite index of the mapping class group of S. This extension acts on H1(\(\widetilde S\)). With a few exceptions for genus 2, we determine the Zariski closure of the image of this representation, and prove that the image is an arithmetic group.