Surfaces, submanifolds, and aligned Fox reimbedding in non-Haken  -manifolds |
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| Authors: | Martin Scharlemann Abigail Thompson |
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| Affiliation: | Department of Mathematics, University of California, Santa Barbara, California 93106 ; Department of Mathematics, University of California, Davis, California 95616 |
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| Abstract: | Understanding non-Haken  -manifolds is central to many current endeavors in  -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  -connected sum decomposition of the submanifold can be aligned with such a structure on the submanifold's complement. |
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