Graphical methods establishing nontriviality of state cycle Khovanov homology classes

Details Graphical methods establishing nontriviality of state cycle Khovanov homology classes Graphical methods establishing nontriviality of state cycle Khovanov homology classes

2009-07-02

arxiv.org/abs/0907.0396v1

Mathematics

Geometric Topology

22 pages, 29 figures

Scientific paper

We determine when certain state cycles represent nontrivial Khovanov homology classes by analyzing features of the state graph. Using this method, we are able to produce hyperbolic knots with arbitrarily many diagonals containing nontrivial state cycle homology classes. This gives lower bounds on the Khovanov width of knots whose complexity precludes computation of the full homology.

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