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Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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
MathSciNet review: 2120271
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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:

[CG]
Casson, A. J.; Gordon, C. McA., Reducing Heegaard splittings. Topology Appl. 27 (1987), no. 3, 275-283. MR 0918537 (89c:57020)

[F]
Fox, Ralph H. On the imbedding of polyhedra in $3$-space. Ann. of Math. (2) 49, (1948). 462-470. MR 0026326 (10:138c)

[H]
Hempel, John, $3$-Manifolds, Ann. Math. Studies 86 (Princeton University Press, Princeton, NJ, 1976). MR 0415619 (54:3702)

[MT]
Menasco, W.; Thompson, A. Compressing handlebodies with holes. Topology 28 (1989), no. 4,

485-494. MR 1030989 (91b:57010)

[ST]
Scharlemann, Martin; Thompson, Abigail, Thin position for $3$-manifolds. Geometric topology (Haifa, 1992), 231-238, Contemp. Math., 164, Amer. Math. Soc., Providence, RI, 1994. MR 1282766 (95e:57032)

[W]
Waldhausen, Friedhelm, Heegaard-Zerlegungen der $3$-Sphäre. (German) Topology 7 1968, 195-203. MR 0227992 (37:3576)

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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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