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

Lobb, Andrew

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


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Abstract

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.

Citation

Lobb, A. (2009). A slice genus lower bound from sl(n) Khovanov-Rozansky homology. Advances in Mathematics, 222(4), 1220-1276. https://doi.org/10.1016/j.aim.2009.06.001

Journal Article Type Article
Publication Date Nov 10, 2009
Deposit Date Oct 18, 2011
Publicly Available Date Feb 21, 2014
Journal Advances in Mathematics
Print ISSN 0001-8708
Publisher Elsevier
Peer Reviewed Peer Reviewed
Volume 222
Issue 4
Pages 1220-1276
DOI https://doi.org/10.1016/j.aim.2009.06.001
Keywords Slice genus lower bound Khovanov–Rozansky homology.
Public URL https://durham-repository.worktribe.com/output/1527089

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Copyright Statement
NOTICE: this is the author’s version of a work that was accepted for publication in Advances in mathematics. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published in Advances in mathematics, 222, 4, 2009, 10.1016/j.aim.2009.06.001





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