A crossed homomorphism for groups acting on the circle

2023/01/18 by Shuhei Maruyama, Maruyama, Shuhei
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Geometric Topology (math.GT) #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2301.07437

openalex publication_date 2023/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We construct a crossed homomorphism by using a group action on the circle and the Poincaré translation number. We relate it to the Euler class of the action in terms of the Hochschild--Serre spectral sequence. As an application, we answer a question of Calegari and Chen, which is on an explicit form of a certain crossed homomorphism on the mapping class group of the sphere minus a Cantor set.

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