Geometriae Dedicata

, Volume 64, Issue 1, pp 69–83

Prym Representations of Mapping Class Groups

  • Eduard Looijenga

DOI: 10.1023/A:1004909416648

Cite this article as:
Looijenga, E. Geometriae Dedicata (1997) 64: 69. doi:10.1023/A:1004909416648


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.

Prym covering mapping class group arithmetic group. 

Copyright information

© Kluwer Academic Publishers 1997

Authors and Affiliations

  • Eduard Looijenga
    • 1
  1. 1.Faculteit Wiskunde en InformaticaRijksuniversiteit UtrechtUtrechtThe Netherlands

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