Prime amphicheiral knots with free period 2

Infinite Order Amphicheiral Knots

In 1977 Gordon [G] asked whether every class of order two in the classical knot concordance group can be represented by an amphicheiral knot. The question remains open although counterexamples in higher dimensions are now known to exist [CM]. This problem is more naturally stated in terms of negative amphicheiral knots, since such knots represent 2–torsion in concordance; that is, if K is negat...

On rational sliceness of Miyazaki’s fibered, −amphicheiral knots

We prove that certain fibered, −amphicheiral knots are rationally slice. Moreover, we show that the concordance invariants ν and Υ(t) from Heegaard Floer homology vanish for a class of knots that includes rationally slice knots.

A Conjecture of Kauuman on Amphicheiral Alternating Knots

We give a counterexample to the following conjecture of Kauuman 2]: Conjecture Let K be an amphicheiral alternating knot. Then there exists a reduced alternating knot-diagram D of K, such that G(D) is isomorphic to G (D), where G(D) is a checkerboard-graph of D and G (D) its dual.

Tait’s Conjectures and Odd Crossing Number Amphicheiral Knots

We give a brief historical overview of the Tait conjectures, made 120 years ago in the course of his pioneering work in tabulating the simplest knots, and solved a century later using the Jones polynomial. We announce the solution, again based on a substantial study of the Jones polynomial, of one (possibly his last remaining?) problem of Tait, with the construction of amphicheiral knots of alm...

A Prime Strongly Positive Amphicheiral Knot Which Is Not Slice