On the Khovanov Homology of Surgeries

TL;DR

This paper introduces a spectral sequence relating the rational Khovanov homology of links to their surgeries, providing a new splitting formula for the Jones polynomial.

Contribution

It develops a spectral sequence framework connecting link surgeries with rational Khovanov homology, offering a novel computational tool.

Findings

Spectral sequence for rational Khovanov homology of links

Explicit splitting formula for the Jones polynomial

Connections between link surgeries and homological invariants

Abstract

We show a spectral sequence for the rational Khovanov homology of an oriented link in terms of the rational Khovanov complexes and homologies of the link surgeries along an admissible cut. As a non trivial corollary, we give an explicit splitting formula for the Jones polynomial.