Observations on Lickorish knotting of contractible 4-manifolds

Charles Livingston

Vol. 209 (2003), No. 2, 319–323

DOI: 10.2140/pjm.2003.209.319

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.

Milestones

Received: 24 November 2001

Revised: 6 January 2002

Published: 1 April 2003