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  1. ; (, Michigan Mathematical Journal)
    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 S1 → X → Sg. There is an exact sequence 1→H1(Sg)→Mod(X)→Mod(Sg)→1. We relate this to the Birman exact sequence and determine when this sequence splits. 
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