Geodesic
A lower bound for the number of group actions on a compact Riemann surface
Anderson, James W1 ; Wootton, Aaron2
1School of Mathematics, University of Southampton, University Road, Southampton, SO17 1BJ, UK
2Department of Mathematics, University of Portland, 5000 North Willamette Blvd, Portland OR 97203, USA
Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 19-35
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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.

DOI : 10.2140/agt.2012.12.19
Classification : 14H37, 57M60, 30F20
Keywords: Riemann surface, automorphism, signature, mapping class group

Anderson, James W  1   ; Wootton, Aaron  2

1 School of Mathematics, University of Southampton, University Road, Southampton, SO17 1BJ, UK
2 Department of Mathematics, University of Portland, 5000 North Willamette Blvd, Portland OR 97203, USA 
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Anderson, James W; Wootton, Aaron. A lower bound for the number of group actions on a compact Riemann surface. Algebraic and Geometric Topology, Tome 12 (2012) no. 1, pp. 19-35. doi: 10.2140/agt.2012.12.19

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