An estimate of infinite cyclic coverings and knot theory

Akio Kawauchi and Takao Matumoto

Vol. 90 (1980), No. 1, 99–103

DOI: 10.2140/pjm.1980.90.99

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 n− 1. 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