The Khovanov homology of (p,-p,q) pretzel knots

Details The Khovanov homology of (p,-p,q) pretzel knots The Khovanov homology of (p,-p,q) pretzel knots

2009-09-10

arxiv.org/abs/0909.1853v3

Mathematics

Geometric Topology

Final version to appear in J. Knot Theory Ramifications

Scientific paper

10.1142/S0218216511010103

In this paper, we compute the Khovanov homology over \Q for (p,-p,q) pretzel knots for odd values of p from 3 to 15 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 and \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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