Surface group representations in ${\rm SL}_2({\mathbb C})$ with finite mapping class orbits
Geometric Topology
2022-06-29 v4 Dynamical Systems
Abstract
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.
Cite
@article{arxiv.1707.00071,
title = {Surface group representations in ${\rm SL}_2({\mathbb C})$ with finite mapping class orbits},
author = {Indranil Biswas and Subhojoy Gupta and Mahan Mj and Junho Peter Whang},
journal= {arXiv preprint arXiv:1707.00071},
year = {2022}
}
Comments
30 pages, 5 figures, accepted for publication in Geometry & Topology