Stabilization of the Khovanov Homotopy Type of Torus Links

Michael Willis

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arXiv · 1511.02742

Stabilization of the Khovanov Homotopy Type of Torus Links

Michael Willis

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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 $m\rightarrow\infty$. 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 $m\rightarrow\infty$. 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 $Sq^2$ action.

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Michael Willis. 2015-11-09. Stabilization of the Khovanov Homotopy Type of Torus Links. https://arxiv.org/abs/1511.02742

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