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THE KHOVANOV HOMOLOGY OF (p, -p, q) PRETZEL KNOTS

LAURA STARKSTON

University of Texas at Austin, Austin, Texas 78712, USA

https://doi.org/10.1142/S0218216511010103Cited by:6 (Source: Crossref)

Abstract

In this paper, we compute the Khovanov homology over ℚ for (p, -p, q) pretzel knots for 3 ≤ p ≤ 15, p odd, and arbitrarily large q. We provide a conjecture for the general form of the Khovanov homology of (p, -p, q) pretzel knots. These computations reveal that these knots have thin Khovanov homology (over ℚ or ℤ). Because Greene has shown that these knots are not quasi-alternating, this provides an infinite class of non-quasi-alternating knots with thin Khovanov homology.

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