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.
Create a lesson
Related papers
Smooth and Topological Nonorientable Four-Genera of Low-Crossing Knots
Seong-Jin Lee
Universal bounds for decompositions of PL manifolds
Rustam Sadykov
A surface-group action on real-hyperbolic space with no Cannon--Thurston map
Bruno Dular
Combination Theorems and the Farrell--Jones Conjecture for Graph Products of Pairs
I. Gkeneralis, S. Prassidis
Multivariable Alexander polynomials of twisted torus links via Dehn surgery
Birch Bryant
Quasimorphisms and bounded cohomology of transformation groups of nonorientable surfaces
Michael Brandenbursky