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

Biswas, Indranil¹ ; Gupta, Subhojoy² ; Mj, Mahan¹ ; Whang, Junho Peter³

¹ School of Mathematics, Tata Institute of Fundamental Research, Mumbai, India
² Department of Mathematics, Indian Institute of Science, Bangalore, India
³ Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, United States

Geometry & topology, Tome 26 (2022) no. 2, pp. 679-719.

Résumé

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.

Détail

DOI : 10.2140/gt.2022.26.679

Keywords: character variety, surface group, mapping class group

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