A Khovanov stable homotopy type

TL;DR

This paper constructs a combinatorial, explicit stable homotopy type for links whose cohomology recovers Khovanov homology, providing a new topological perspective on link invariants.

Contribution

It introduces a combinatorial and explicit construction of spectra representing Khovanov homology, dependent only on the link's isotopy class.

Findings

Spectra X^j(L) are constructed for each link diagram.

Khovanov homology is isomorphic to the cohomology of X^j(L).

Homotopy type depends only on the link isotopy class.

Abstract

Given a link diagram L we construct spectra X^j(L) so that the Khovanov homology Kh^{i,j}(L) is isomorphic to the (reduced) singular cohomology H^i(X^j(L)). The construction of X^j(L) is combinatorial and explicit. We prove that the homotopy type of X^j(L) depends only on the isotopy class of the corresponding link.