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

A lower bound for the number of group actions on a compact riemann surface
A lower bound for the number of group actions on a compact riemann surface
We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus g (at least 2) is at least quadratic in g. We do this through the introduction of a coarse signature space, the space K_g of skeletal signatures of group actions on compact Riemann surfaces of genus g. We discuss the basic properties of K_g and present a full conjectural description.
1472-2747
19-35
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Wootton, Aaron
46e76a19-aae5-4f6f-a353-211d66009015
Anderson, James W.
739c0e33-ef61-4502-a675-575d08ee1a98
Wootton, Aaron
46e76a19-aae5-4f6f-a353-211d66009015

Anderson, James W. and Wootton, Aaron (2012) A lower bound for the number of group actions on a compact riemann surface. Algebraic & Geometric Topology, 12 (1), 19-35. (doi:10.2140/agt.2012.12.19).

Record type: Article

Abstract

We prove that the number of distinct group actions on compact Riemann surfaces of a fixed genus g (at least 2) is at least quadratic in g. We do this through the introduction of a coarse signature space, the space K_g of skeletal signatures of group actions on compact Riemann surfaces of genus g. We discuss the basic properties of K_g and present a full conjectural description.

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Submitted date: July 2011
Accepted/In Press date: October 2011
Published date: January 2012
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 196515
URI: https://eprints.soton.ac.uk/id/eprint/196515
ISSN: 1472-2747
PURE UUID: 4fdedc30-069d-484f-8b96-ed117ab80294
ORCID for James W. Anderson: ORCID iD orcid.org/0000-0002-7849-144X

Catalogue record

Date deposited: 08 Sep 2011 09:27
Last modified: 20 Jul 2019 01:17

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