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

Author(s): Hee Jung Kim; Daniel Ruberman
Journal: Trans. Amer. Math. Soc. 360 (2008), 5869-5881.
MSC (2000): Primary 57R57
Posted: June 26, 2008
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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: 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
Posted: June 26, 2008
Additional Notes: The second author was partially supported by NSF Grant 0505605.
Copyright of article: Copyright 2008, American Mathematical Society

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