Observations on Lickorish knotting of contractible 4-manifolds

Charles Livingston

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Observations on Lickorish knotting of contractible 4-manifolds

Charles Livingston

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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.

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BibTeX RIS

Charles Livingston. 2001-11-06. Observations on Lickorish knotting of contractible 4-manifolds. https://arxiv.org/abs/math/0111065

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