Volume 12, issue 1 (2012)

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ISSN (electronic): 1472-2739
ISSN (print): 1472-2747
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
Abstract

We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus σ 2 is at least quadratic in σ. We do this through the introduction of a coarse signature space, the space Kσ of skeletal signatures of group actions on compact Riemann surfaces of genus σ. We discuss the basic properties of Kσ 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/