Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken 3-manifolds

Scharlemann, Martin; Thompson, Abigail

doi:10.1090/S0002-9939-04-07704-4

Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken $3$-manifolds
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by Martin Scharlemann and Abigail Thompson PDF

Proc. Amer. Math. Soc. 133 (2005), 1573-1580 Request permission

Abstract:

Understanding non-Haken $3$-manifolds is central to many current endeavors in $3$-manifold topology. We describe some results for closed orientable surfaces in non-Haken manifolds, and extend Fox’s theorem for submanifolds of the 3-sphere to submanifolds of general non-Haken manifolds. In the case where the submanifold has connected boundary, we show also that the $\partial$-connected sum decomposition of the submanifold can be aligned with such a structure on the submanifold’s complement.

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