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Surface group representations in SL2(C) with finite mapping class orbits

Biswas, I and Gupta, S and Mj, M and Whang, JP (2022) Surface group representations in SL2(C) with finite mapping class orbits. In: Geometry and Topology, 26 (2). pp. 679-719.

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Official URL: https://doi.org/10.2140/gt.2022.26.679


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 homo-morphisms 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.

Item Type: Journal Article
Publication: Geometry and Topology
Publisher: Mathematical Sciences Publishers
Additional Information: The copyright for this article belongs to the Authors.
Department/Centre: Division of Physical & Mathematical Sciences > Mathematics
Date Deposited: 21 Jul 2022 05:19
Last Modified: 21 Jul 2022 05:19
URI: https://eprints.iisc.ac.in/id/eprint/74961

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