English

Observations on Lickorish knotting of contractible 4-manifolds

Geometric Topology 2007-05-23 v1

Abstract

Lickorish has constructed large families of contractible 4--manifolds that have knotted embeddings in the 4--sphere and has also shown that every finitely presented perfect group with balanced presentation occurs as the fundamental group of the complement of a knotted contractible manifold. Here we make a few observations regarding Lickorish's construction, showing how to extend it to construct contractible 4--manifolds which have an infinite number of knotted embeddings and also to construct knotted embeddings of the Mazur manifold for which the complement has trivial fundamental group.

Keywords

Cite

@article{arxiv.math/0111065,
  title  = {Observations on Lickorish knotting of contractible 4-manifolds},
  author = {Charles Livingston},
  journal= {arXiv preprint arXiv:math/0111065},
  year   = {2007}
}

Comments

4 pages, 1 figure