Strongly Invertible Knots and Sutured Khovanov Homology

Michael Snape (University of Glasgow)

Monday 31st October, 2016 15:00-16:00 Maths 204

Abstract

A strongly invertible knot is a knot in the 3-sphere along with an orientation preserving involution of S^3 that reverses the orientation of the knot. By extending a construction developed by Makoto Sakuma in the 1980's it is possible to associate to each strongly invertible knot a pair of knots in the thickened annulus A times I. These form an interesting class of examples in light of recent developments in Khovanov and Heegaard-Floer style homology theories. In particular, a variation of Khovanov homology for knots in annuli --- known as sutured Khovanov homology --- can be applied with relative ease. As well as being a detector of strong inversions, sutured Khovanov homology is of interest because of its relation to sutured Floer homology and Khovanov homology via spectral sequences. In this talk I will first outline Sakuma's construction and sutured Khovanov homology, and then will provide some explicit calculations. In addition, time permitting, I will go on to describe the relationship between sutured Khovanov homology and sutured Floer homology

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