Almost-extreme Khovanov spectra

TL;DR

This paper introduces a new functor related to Khovanov spectra, providing a decomposition that enables computation of the homotopy type for certain knot diagrams, advancing understanding in knot homology.

Contribution

It presents a functor from the cube to the Burnside 2-category equivalent to the almost-extreme Khovanov spectrum and offers a decomposition into simplicial complexes for computational purposes.

Findings

Computed homotopy types for non-alternating diagrams

Established equivalence with Lipshitz and Sarkar's Khovanov spectrum

Provided a new decomposition method for these spectra

Abstract

We introduce a functor from the cube to the Burnside 2-category and prove that it is equivalent to the Khovanov spectrum given by Lipshitz and Sarkar in the almost-extreme quantum grading. We provide a decomposition of this functor into simplicial complexes. This decomposition allows us to compute the homotopy type of the almost-extreme Khovanov spectra of diagrams without alternating pairs.