Algebraic Mapping Class Group Rigidity

2025/08/13 by Seong Youn Kim, Kim, Seong Youn
#math.GT

paper · pdf · doi:10.48550/arxiv.2508.09421

Abstract

Let g, n ≥ 0 and Σ= Σ_{g, n} be a connected oriented surface of genus g with n punctures. The SL₂-character variety of Σ has a rigid relative automorphism group, whose elements fix each monodromies along punctures, and is a finite extension of the mapping class group. The exceptional isomorphism between the SL(2, ℂ)-character variety and moduli of points on complex 3-sphere provides a new description of the mapping class group of certain Σ.

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