Realizing concordant polynomials with prime knots

Steven Albert Bleiler

Vol. 100 (1982), No. 2, 249–257

DOI: 10.2140/pjm.1982.100.249

Abstract

This paper employs the theory of tangles to show that every knot in the 3-sphere is concordant to a prime knot with the same Alexander polynomial. From this it is shown that all algebraic concordances at the polynomial level are realized by geometric concordances between prime knots.

Mathematical Subject Classification 2000

Primary: 57M25

Milestones

Received: 8 August 1980

Published: 1 June 1982