Topological triviality of smoothly knotted surfaces in 4-manifolds
Geometric Topology
2008-10-21 v2 Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.math/0610204,
title = {Topological triviality of smoothly knotted surfaces in 4-manifolds},
author = {Hee Jung Kim and Daniel Ruberman},
journal= {arXiv preprint arXiv:math/0610204},
year = {2008}
}
Comments
Final version; appeared in AMS Transactions. 15 pages, 2 figures