Algebraic and Geometric Topology 1 (2001), paper no. 11, pages 231-241.

Infinite Order Amphicheiral Knots

Charles Livingston

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

AMS subject classification. Primary: 57M25. Secondary: 57M27.

DOI: 10.2140/agt.2001.1.231

E-print: arXiv:math.GT/0008166

Submitted: 17 December 2000. Accepted: 12 April 2001. Published: 16 April 2001.

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Charles Livingston
Department of Mathematics, Indiana University
Bloomington, IN 47405, USA
Email: livingst@indiana.edu

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