A Khovanov Laplacian and Khovanov Dirac for Knots and Links

Published 28 Nov 2024 in math.GT and math.AT | (2411.18841v2)

Abstract: Khovanov homology has been the subject of much study in knot theory and low dimensional topology since 2000. This work introduces a Khovanov Laplacian and a Khovanov Dirac to study knot and link diagrams. The harmonic spectrum of the Khovanov Laplacian or the Khovanov Dirac retains the topological invariants of Khovanov homology, while their non-harmonic spectra reveal additional information that is distinct from Khovanov homology.

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