Periodicity, genera and Alexander polynomials of knots

Swatee Naik

Vol. 166 (1994), No. 2, 357–371

DOI: 10.2140/pjm.1994.166.357

Abstract

For knots in S³ criteria for periodicity are obtained in terms of the homology groups of cyclic branched covers of S³ and the Alexander polynomial. Also the relationship between the genus of a periodic knot and the Alexander polynomial is studied. As an application it is shown that no eleven crossing knot has a period greater than 5.

Mathematical Subject Classification 2000

Primary: 57M25

Milestones

Received: 13 August 1992

Revised: 5 May 1993

Accepted: 14 June 1993

Published: 1 December 1994