Hyperbolic Knots and Torsion in Khovanov Homology

2022/05/16 by Micah Chrisman, Sujoy Mukherjee, Chrisman, Micah +1
Mathematics · #57K10 #57K18 #57K32 #FOS: Mathematics #Geometric Topology (math.GT) #Geometric and Algebraic Topology #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2205.07747

openalex publication_date 2022/05/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we show that if there is a knot in S³ having ℤ_m torsion in its Khovanov homology, then there are infinitely many hyperbolic knots and infinitely many prime satellite knots having ℤ_m torsion in their Khovanov homology. As an application, we give the first known examples of hyperbolic knots and links with odd (and other non-ℤ₂ torsion) in their Khovanov homology.

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