Topological triviality of smoothly knotted surfaces in 4-manifolds

Hee Jung Kim; Daniel Ruberman

doi:10.1090/s0002-9947-08-04482-6

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Topological triviality of smoothly knotted surfaces in 4-manifolds

Hee Jung Kim·Daniel Ruberman

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Abstract

Some generalizations and variations of the Fintushel-Stern rim surgery are known to produce smoothly knotted surfaces. We show that if the fundamental groups of their complements are cyclic, then these surfaces are topologically unknotted. Using a twist-spinning construction from high-dimensional knot theory, we construct examples of knotted surfaces whose complements have cyclic fundamental groups.

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BibTeX RIS

Hee Jung Kim, Daniel Ruberman. 2008-10-21. Topological triviality of smoothly knotted surfaces in 4-manifolds. https://doi.org/10.1090/s0002-9947-08-04482-6

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