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.References
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Additional Information
- Martin Scharlemann
- Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
- MR Author ID: 155620
- Email: mgscharl@math.ucsb.edu
- Abigail Thompson
- Affiliation: Department of Mathematics, University of California, Davis, California 95616
- MR Author ID: 172260
- Email: thompson@math.ucdavis.edu
- Received by editor(s): September 28, 2003
- Received by editor(s) in revised form: February 10, 2004
- Published electronically: December 6, 2004
- Additional Notes: This research was supported in part by NSF grants.
- Communicated by: Ronald A. Fintushel
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 133 (2005), 1573-1580
- MSC (2000): Primary 11Y16, 57M50; Secondary 57M25
- DOI: https://doi.org/10.1090/S0002-9939-04-07704-4
- MathSciNet review: 2120271