A short proof of Greenberg’s Theorem
A short proof of Greenberg’s Theorem
Greenberg proved that every countable group A is isomorphic to the automorphism group of a Riemann surface, which can be taken to be compact if A is finite. We give a short and explicit algebraic proof of this for finitely generated groups A.
Automorphism group, Finitely generated group, Fuchsian group, Greenberg’s Theorem, Non-arithmetic group, Riemann surface, Triangle group
83-88
American Mathematical Society
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
2022
Jones, Gareth A.
fdb7f584-21c5-4fe4-9e57-b58c78ebe3f5
Jones, Gareth A.
(2022)
A short proof of Greenberg’s Theorem.
In,
Wootton, Aaron, Broughton, S. Allen and Paulhus, Jennifer
(eds.)
Automorphisms of Riemann Surfaces, Subgroups of Mapping Class Groups and Related Topics.
(Contemporary Mathematics, 776)
American Mathematical Society, .
(doi:10.1090/conm/776/15608).
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Abstract
Greenberg proved that every countable group A is isomorphic to the automorphism group of a Riemann surface, which can be taken to be compact if A is finite. We give a short and explicit algebraic proof of this for finitely generated groups A.
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Published date: 2022
Additional Information:
Publisher Copyright:
© 2022 American Mathematical Society.
Copyright:
Copyright 2022 Elsevier B.V., All rights reserved.
Keywords:
Automorphism group, Finitely generated group, Fuchsian group, Greenberg’s Theorem, Non-arithmetic group, Riemann surface, Triangle group
Identifiers
Local EPrints ID: 474845
URI: http://eprints.soton.ac.uk/id/eprint/474845
ISSN: 0271-4132
PURE UUID: d7b36001-c64a-484a-a524-a36843dcd6e2
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Date deposited: 03 Mar 2023 17:46
Last modified: 17 Mar 2024 01:12
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Contributors
Author:
Gareth A. Jones
Editor:
Aaron Wootton
Editor:
S. Allen Broughton
Editor:
Jennifer Paulhus
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