Stabilization of the Khovanov Homotopy Type of Torus Links

Abstract

The structure of the Khovanov homology of $(n,m)$ torus links has been extensively studied. In particular, Marko Stosic proved that the homology groups stabilize as $m\to \infty$. We show that the Khovanov homotopy types of $(n,m)$ torus links, as constructed by Robert Lipshitz and Sucharit Sarkar, also become stably homotopy equivalent as $m\to \infty$. We provide an explicit bound on values of $m$ beyond which the stabilization begins. As an application, we give new examples of torus links with non-trivial $S{q}^2$ action.

arXiv comment17 pages, 6 figures