Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Martin Scharlemann and Abigail Thompson
Journal: Proc. Amer. Math. Soc. 133 (2005), 1573-1580
MSC (2000): Primary 11Y16, 57M50; Secondary 57M25
Published electronically: December 6, 2004
MathSciNet review: 2120271
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 11Y16, 57M50, 57M25

Retrieve articles in all journals with MSC (2000): 11Y16, 57M50, 57M25


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: http://dx.doi.org/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
Published electronically: December 6, 2004
Additional Notes: This research was supported in part by NSF grants.
Communicated by: Ronald A. Fintushel
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.