Vol. 90, No. 1, 1980

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An estimate of infinite cyclic coverings and knot theory

Akio Kawauchi and Takao Matumoto

Vol. 90 (1980), No. 1, 99–103
Abstract

In this paper we estimate the homology torsion module of an infinite cyclic covering space of an n-manifold by the homology of a Poincaré duality space of dimension n1. To be concrete, we apply it to knot theory. In particular, it follows that any ribbon n-knot K Sn+2 (n 3) is unknotted if π1(Sn+2 K)Z. We add also in this paper a somewhat geometric proof to this unknotting criterion.

Mathematical Subject Classification 2000
Primary: 57Q45
Milestones
Received: 25 September 1979
Published: 1 September 1980
Authors
Akio Kawauchi
Takao Matumoto