On a family of unitary representations of mapping class groups

2019/06/04 by Biao Ma, Ma, Biao
Mathematics · #Advanced Algebra and Geometry #Dynamical Systems (math.DS) #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1906.01326

openalex publication_date 2019/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a compact surface S = S_g,n with 3g + n ≥ 4, we introduce a family of unitary representations of the mapping class group Mod(S) based on the space of measured foliations. For this family of representations, we show that none of them has almost invariant vectors. As one application, we obtain an inequality concerning the action of Mod(S) on the Teichmüller space of S. Moreover, using the same method plus recent results about weak equivalence, we also give a classification, up to weak equivalence, for the unitary quasi-representations with respect to geometrical subgroups.

Related

• Representations of surface groups with finite mapping class group orbits
• The Nielsen Realization Problem for Non-Orientable Surfaces
• Linear representations of the mapping class group of dimension at most 3g-3
• Canonical representations of surface groups
• Ergodic actions of mapping class groups on moduli spaces of representations of non-orientable surfaces