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Surface group
representations in ${\rm SL}_2(\mathbb{C})$ with finite
mapping class orbits
Indranil Biswas, Subhojoy Gupta, Mahan Mj and Junho Peter Whang |
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Geometry & Topology 26 (2022) 679–719
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Abstract |
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Given an oriented surface of positive genus with finitely many punctures, we classify the finite orbits of the mapping class group action on the moduli space of semisimple complex special linear two dimensional representations of the fundamental group of the surface. For surfaces of genus at least two, such orbits correspond to homomorphisms with finite image. For genus one, they correspond to the finite or special dihedral representations. We also obtain an analogous result for bounded orbits in the moduli space. |
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Keywords
character variety, surface group, mapping class group
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Mathematical Subject Classification
Primary: 57M50
Secondary: 57M05, 20E36, 20F29
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References |
Publication
Received: 17 April 2020
Revised: 3 March 2021
Accepted: 10 April 2021
Published: 15 June 2022
Proposed: David M Fisher
Seconded: Ulrike Tillmann, Benson Farb
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Authors |
| Indranil Biswas | |
| School of Mathematics Tata Institute of Fundamental Research Mumbai India |
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| Subhojoy Gupta | |
| Department of Mathematics Indian Institute of Science Bangalore India |
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| Mahan Mj | |
| School of Mathematics Tata Institute of Fundamental Research Mumbai India |
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| Junho Peter Whang | |
| Department of Mathematics Massachusetts Institute of Technology Cambridge, MA United States |
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