Topological triviality of smoothly knotted surfaces in 4-manifolds

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

2006-10-06

arxiv.org/abs/math/0610204v2

Trans. Amer. Math. Soc. 360 (2008), 5869-5881

Mathematics

Geometric Topology

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

Scientific paper

10.1090/S0002-9947-08-04482-6

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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