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On mapping class groups of contractible open $ 3$-manifolds


Author: Robert Myers
Journal: Trans. Amer. Math. Soc. 335 (1993), 1-46
MSC: Primary 57N10; Secondary 57M99, 57R50, 57R52, 57S05
DOI: https://doi.org/10.1090/S0002-9947-1993-1069740-9
MathSciNet review: 1069740
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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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Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1069740-9
Keywords: $ 3$-manifold, mapping class group, isotopy, Whitehead manifold, eventually end-irreducible
Article copyright: © Copyright 1993 American Mathematical Society

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