Torsion in Khovanov homology of homologically thin knots

2018/06/13 by Shumakovitch, Alexander N. · 2 citations
#57M25 #57M27 #Algebraic Topology (math.AT) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.1806.05168

Abstract

We prove that every ℤ₂H-thin link has no 2^k-torsion for k>1 in its Khovanov homology. Together with previous results by Eun Soo Lee and the author, this implies that integer Khovanov homology of non-split alternating links is completely determined by the Jones polynomial and signature. Our proof is based on establishing an algebraic relation between Bockstein and Turner differentials on Khovanov homology over ℤ₂. We conjecture that a similar relation exists between the corresponding spectral sequences.

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• On detection probabilities of link invariants
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