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Compatible pants decompositions for SL2(ℂ)-representations of surface groups

2022/10/18 by Renaud Detcherry, Detcherry, Renaud, Thomas Le Fils +3
Mathematics · #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric Topology (math.GT) #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2210.09854

openalex publication_date 2022/10/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For any irreducible representation of a surface group into SL2(ℂ), we show that there exists a pants decomposition where the restriction to any pair of pants is irreducible and where no curve of the decomposition is sent to a trace ± 2 element. We prove a similar property for SO3-representations. We also investigate the type of pants decomposition that can occur in this setting for a given representation. This result was announced in a previous paper of the first and third named authors, motivated by the study of the Azumaya locus of the skein algebra of surfaces at roots of unity.

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