Mapping class groups of circle bundles over a surface

Bena Tshishiku; Lei Chen

Mapping class groups of circle bundles over a surface

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arxiv 2301.05375 v1 pith:UALHPRYI submitted 2023-01-13 math.GT math.GR

Mapping class groups of circle bundles over a surface

Lei Chen , Bena Tshishiku This is my paper

classification math.GT math.GR

keywords rightarrowsequencecircleclassexactmappingsurfacealgebraic

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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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