The homotopy theory of Khovanov homology

TL;DR

This paper provides a homotopy theoretic interpretation of unnormalized Khovanov homology by identifying it with derived functors of the inverse limit, offering a new perspective on link invariants.

Contribution

It introduces a novel homotopy theoretic framework for understanding Khovanov homology through derived functors and inverse limits.

Findings

Khovanov homology can be realized as derived functors of inverse limits.

Provides a homotopy-theoretic interpretation of link invariants.

Establishes connections between algebraic and topological methods in knot theory.

Abstract

We show that the unnormalised Khovanov homology of an oriented link can be identified with the derived functors of the inverse limit. This leads to a homotopy theoretic interpretation of Khovanov homology.