A crossed homomorphism for groups acting on the circle
Geometric Topology
2023-03-17 v3
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.
Keywords
Cite
@article{arxiv.2301.07437,
title = {A crossed homomorphism for groups acting on the circle},
author = {Shuhei Maruyama},
journal= {arXiv preprint arXiv:2301.07437},
year = {2023}
}
Comments
10 pages, no figures; title and main theorem changed