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Non-quasi-alternating Montesinos links, and lens space surgeries on knots
by
Josh Greene
Princeton University
I will discuss some examples of links whose non-quasi-alternating-ness can be established by the study of negative definite 4-manifolds, by contrast to homological width. In particular, some of these examples have thin knot Floer and reduced Khovanov homology. Whether their odd Khovanov homology is thin remains to be seen (though I may know more when I speak). As a related application, I will show that if p is positive integer, and p-surgery on a knot gives a lens space, then the knot genus is bounded above by (p -√(cp))/2 for some absolute constant c between 1.5 and 4. For p large, this improves on a conjectured bound by Goda and Teragaito.
Date received: December 29, 2008
Copyright © 2008 by the author(s). The author(s) of this work and the organizers of the conference have granted their consent to include this abstract in Topology Atlas. Document # caxq-61.