A slice genus lower bound from sl ( n ) Khovanov–Rozansky homology

We show that a generic perturbation of the doubly-graded Khovanov–Rozansky knot homology gives rise to a lower-bound on the slice genus of a knot. We prove a theorem about obtainable presentations of surfaces embedded in 4-space, which we use to simplify significantly our algebraic computations.

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Bibliographic Details
Published in:Advances in mathematics (New York. 1965) 2009-11, Vol.222 (4), p.1220-1276
Main Author: Lobb, Andrew
Format: Article
Language:English
Subjects:
Slice genus lower bound Khovanov–Rozansky homology
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Summary:We show that a generic perturbation of the doubly-graded Khovanov–Rozansky knot homology gives rise to a lower-bound on the slice genus of a knot. We prove a theorem about obtainable presentations of surfaces embedded in 4-space, which we use to simplify significantly our algebraic computations.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2009.06.001