Infinite order amphicheiral knots

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

References

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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

Volume 1, issue 1 (2001)

Charles Livingston