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

Author(s): Martin Scharlemann; Abigail Thompson
Journal: Proc. Amer. Math. Soc. 133 (2005), 1573-1580.
MSC (2000): Primary 11Y16, 57M50; Secondary 57M25
Posted: December 6, 2004
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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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Additional Information:

Martin Scharlemann
Affiliation: Department of Mathematics, University of California, Santa Barbara, California 93106
Email: mgscharl@math.ucsb.edu

Abigail Thompson
Affiliation: Department of Mathematics, University of California, Davis, California 95616
Email: thompson@math.ucdavis.edu

DOI: 10.1090/S0002-9939-04-07704-4
PII: S 0002-9939(04)07704-4
Received by editor(s): September 28, 2003
Received by editor(s) in revised form: February 10, 2004
Posted: December 6, 2004
Additional Notes: This research was supported in part by NSF grants.
Communicated by: Ronald A. Fintushel
Copyright of article: Copyright 2004, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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