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Infinite order amphicheiral knots

Charles Livingston

Algebraic & Geometric Topology 1 (2001) 231–241

arXiv: math.GT/0008166

Abstract

In answer to a question of Long, Flapan constructed an example of a prime strongly positive amphicheiral knot that is not slice. Long had proved that all such knots are algebraically slice. Here we show that the concordance group of algebraically slice knots contains an infinitely generated free subgroup that is generated by prime strongly positive amphicheiral knots. A simple corollary of this result is the existence of positive amphicheiral knots that are not of order two in concordance.

Keywords
knot, amphicheiral, concordance, infinite order
Mathematical Subject Classification 2000
Primary: 57M25
Secondary: 57M27
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Publication
Received: 17 December 2000
Accepted: 12 April 2001
Published: 16 April 2001
Authors
Charles Livingston
Department of Mathematics
Indiana University
Bloomington IN 47405
USA