Topological triviality of smoothly knotted surfaces in 4-manifolds
Abstract
Description
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.
Final version; appeared in AMS Transactions. 15 pages, 2 figures
Final version; appeared in AMS Transactions. 15 pages, 2 figures