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An embedding for π2 of a subcomplex of a finite contractible two-complex

Published online by Cambridge University Press:  18 May 2009

William A. Bogley
William A. Bogley
Affiliation:
Department of Mathematics, Oregon State University, Corvallis OR 97331, USA
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A longstanding open question in low dimensional topology was raised by J. H. C. Whitehead in 1941 [9]: “Is any subcomplex of an aspherical, two-dimensional complex itself aspherical?” The asphericity of classical knot complements [7] provides evidence that the answer to Whitehead's question might be “yes”. Indeed, each classical knot complement has the homotopy type of a two-complex which can be embedded in a finite contractible two-complex. This property is shared by a large class of four-manifolds; these are the ribbon disc complements, whose asphericity has been conjectured, and even claimed, but never proven. (See [4] for a discussion.) It is reasonable and convenient to formulate the following.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 3 , September 1991 , pp. 365 - 371
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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