Extreme Khovanov spectra

TL;DR

This paper proves that a spectrum constructed by previous researchers is stably homotopy equivalent to the Khovanov spectrum at its extreme quantum grading, linking two important constructions in knot theory.

Contribution

It establishes a stable homotopy equivalence between two different Khovanov spectra at the extreme quantum grading, clarifying their relationship.

Findings

The spectrum by González-Meneses, Manchón, and the second author matches Lipshitz and Sarkar's Khovanov spectrum at the extreme grading.

The result provides a deeper understanding of the homotopy types associated with knot invariants.

The equivalence simplifies the comparison of different spectral constructions in knot theory.

Abstract

We prove that the spectrum constructed by Gonz\'alez-Meneses, Manch\'on and the second author is stably homotopy equivalent to the Khovanov spectrum of Lipshitz and Sarkar at its extreme quantum grading.