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High dimensional knot groups which are not two-knot groups

Published online by Cambridge University Press:  17 April 2009

Jonathan A. Hillman
Jonathan A. Hillman
Affiliation:
Department of Mathematics, School of General Studies, Australian National University, Canberra, ACT.
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Abstract

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This paper presents three arguments, one involving orientability, and the others Milnor duality and, respectively, the injectivity of cup product into H2 for an abelian group and free finite group actions on homotopy 3-spheres to show that there are high dimensional knot groups which are not the groups of knotted 2-spheres in S4, thus answering a question of Fox (“Some problems in knot theory”, Topology of 3-manifolds and related topics”, 168–176 (Proceedings of the University of Georgia Institute, 1961. Prentice-Hall, Englewood Cliffs, New Jersey, 1962).

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 16 , Issue 3 , June 1977 , pp. 449 - 462
Copyright
Copyright © Australian Mathematical Society 1977

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