Mapping class groups of circle bundles over a surface

Lei Chen; Bena Tshishiku

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arXiv · 2301.05375

Mapping class groups of circle bundles over a surface

Lei Chen·Bena Tshishiku

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Abstract

In this paper, we study the algebraic structure of mapping class group $Mod(X)$ of 3-manifolds $X$ that fiber as a circle bundle over a surface $S^1\rightarrow X\rightarrow S_g$. There is an exact sequence $1\rightarrow H^1(S_g)\rightarrow Mod(X)\rightarrow Mod(S_g)\rightarrow1$. We relate this to the Birman exact sequence and determine when this sequence splits.

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Lei Chen, Bena Tshishiku. 2023-01-13. Mapping class groups of circle bundles over a surface. https://arxiv.org/abs/2301.05375

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