Unicellular dessins and a uniqueness theorem for Klein's Riemann surface of genus 3
Unicellular dessins and a uniqueness theorem for Klein's Riemann surface of genus 3
If we consider the 14-sided hyperbolic polygon of Felix Klein that defines his famous surface of genus 3, we have a unifacial dessin whose automorphism group is transitive on the edges but not on the directed edges of the dessin. We show that Klein's surface is the unique platonic surface with this property.
701-710
Singerman, David
3eeb0783-c87c-4405-81d7-e80ae4c15f8b
2001
Singerman, David
3eeb0783-c87c-4405-81d7-e80ae4c15f8b
Singerman, David
(2001)
Unicellular dessins and a uniqueness theorem for Klein's Riemann surface of genus 3.
Bulletin of the London Mathematical Society, 33 (6), .
(doi:10.1112/S0024609301008347).
Abstract
If we consider the 14-sided hyperbolic polygon of Felix Klein that defines his famous surface of genus 3, we have a unifacial dessin whose automorphism group is transitive on the edges but not on the directed edges of the dessin. We show that Klein's surface is the unique platonic surface with this property.
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Published date: 2001
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Local EPrints ID: 29803
URI: http://eprints.soton.ac.uk/id/eprint/29803
ISSN: 0024-6093
PURE UUID: 470412fe-bbee-4d4a-aaa3-383abee786ba
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Date deposited: 11 May 2006
Last modified: 15 Mar 2024 07:35
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