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

Lobb, Andrew

doi:10.1016/j.aim.2009.06.001

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

Lobb, Andrew

Authors

Professor Andrew Lobb andrew.lobb@durham.ac.uk
Professor

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.

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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