A lower bound for the number of group actions on a compact Riemann surface

Anderson, James W; Wootton, Aaron

doi:10.2140/agt.2012.12.19

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A lower bound for the number of group actions on a compact Riemann surface

James W Anderson and Aaron Wootton

Algebraic & Geometric Topology 12 (2012) 19–35

DOI: 10.2140/agt.2012.12.19

Abstract

We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus $σ \geq 2$ is at least quadratic in $σ$ . We do this through the introduction of a coarse signature space, the space $K_{σ}$ of skeletal signatures of group actions on compact Riemann surfaces of genus $σ$ . We discuss the basic properties of $K_{σ}$ and present a full conjectural description.

Keywords

Riemann surface, automorphism, signature, mapping class group

Mathematical Subject Classification 2010

Primary: 14H37

Secondary: 57M60, 30F20

References

Publication

Received: 18 July 2011

Accepted: 11 October 2011

Published: 13 January 2012

Authors

James W Anderson
School of Mathematics University of Southampton University Road Southampton SO17 1BJ UK
http://www.soton.ac.uk/maths/about/staff/jwa.page
Aaron Wootton
Department of Mathematics University of Portland 5000 North Willamette Blvd Portland OR 97203 USA
http://faculty.up.edu/wootton/

Volume 12, issue 1 (2012)