A crossed homomorphism for groups acting on the circle

Shuhei Maruyama

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arXiv · 2301.07437

A crossed homomorphism for groups acting on the circle

Shuhei Maruyama

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Abstract

We construct a crossed homomorphism by using a group action on the circle and the Poincar\'{e} 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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Shuhei Maruyama. 2023-01-18. A crossed homomorphism for groups acting on the circle. https://arxiv.org/abs/2301.07437

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