English

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