Khovanov homotopy types and the Dold-Thom functor

TL;DR

This paper demonstrates that a certain Khovanov homotopy type spectrum is a product of Eilenberg-MacLane spaces, linking it directly to Khovanov homology, and shows how it can be derived from Lipshitz and Sarkar's construction using the Dold-Thom functor.

Contribution

It establishes that the Khovanov homotopy type spectrum is a product of Eilenberg-MacLane spaces and connects different constructions via the Dold-Thom functor.

Findings

The spectrum by Everitt and Turner is a product of Eilenberg-MacLane spaces.

The spectrum is determined by Khovanov homology.

It can be obtained from Lipshitz and Sarkar's construction using the Dold-Thom functor.

Abstract

We show that the spectrum constructed by Everitt and Turner as a possible Khovanov homotopy type is a product of Eilenberg-MacLane spaces and is thus determined by Khovanov homology. By using the Dold-Thom functor it can therefore be obtained from the Khovanov homotopy type constructed by Lipshitz and Sarkar.