On mapping class groups of contractible open 3-manifolds

Myers, Robert

doi:10.1090/S0002-9947-1993-1069740-9

On mapping class groups of contractible open $3$-manifolds
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Trans. Amer. Math. Soc. 335 (1993), 1-46 Request permission

Abstract:

Let $W$ be an irreducible, eventually end-irreducible contractible open $3$-manifold other than ${{\mathbf {R}}^3}$, and let $V$ be a "good" exhaustion of $W$. Let $\mathcal {H}(W;V)$ be the subgroup of the mapping class group $\mathcal {H}(W)$ which is "eventually carried by $V$." This paper shows how to compute $\mathcal {H}(W;V)$ in terms of the mapping class groups of certain compact $3$-manifolds associated to $V$. The computation is carried out for a genus two example and for the classical genus one example of Whitehead. For these examples $\mathcal {H}(W) = \mathcal {H}(W;V)$.

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