Topological triviality of smoothly knotted surfaces in 4-manifolds

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.

arXiv commentFinal version; appeared in AMS Transactions. 15 pages, 2 figures

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