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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Topological triviality of smoothly knotted surfaces in $ 4$-manifolds


Authors: Hee Jung Kim and Daniel Ruberman
Journal: Trans. Amer. Math. Soc. 360 (2008), 5869-5881
MSC (2000): Primary 57R57
Published electronically: June 26, 2008
MathSciNet review: 2425695
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Abstract: Some generalizations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are standard, then these surfaces are topologically unknotted.


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Additional Information

Hee Jung Kim
Affiliation: Department of Mathematics, Louisiana State University, Baton Rouge, Louisiana 70803-4918
Email: heekim@lsu.edu

Daniel Ruberman
Affiliation: Department of Mathematics, MS 050, Brandeis University, Waltham, Massachusetts 02454
Email: ruberman@brandeis.edu

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04482-6
PII: S 0002-9947(08)04482-6
Keywords: Rim surgery, knotted surface, surgery theory
Received by editor(s): October 4, 2006
Published electronically: June 26, 2008
Additional Notes: The second author was partially supported by NSF Grant 0505605.
Article copyright: © Copyright 2008 American Mathematical Society