Observations on Lickorish knotting of contractible 4-manifolds

Details Observations on Lickorish knotting of contractible 4-manifolds Observations on Lickorish knotting of contractible 4-manifolds

2001-11-06

arxiv.org/abs/math/0111065v1

Pac. J. of Math 209, (2003), 319-324.

Mathematics

Geometric Topology

4 pages, 1 figure

Scientific paper

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.

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