Filtering Lipshitz-Sarkar homotopy types
Patrick Orson (University of Durham)
Monday 21st September, 2015 16:00-17:00 Maths 522
Khovanov homology is a combinatorially defined knot invariant categorifying the Jones polynomial. In a recent paper, Lipshitz and Sarkar constructed a CW complex whose reduced homology returns Khovanov homology and whose stable homotopy type is a knot invariant. Astonishingly, the stable homotopy type is a finer invariant than the homology in some cases. In this talk we will describe our attempts to extend the Lipshitz-Sarkar machine to find space-level meaning for the filtrations of the Khovanov chain complex that give rise to various spectral sequences relating Khovanov homology other knot homology theories. No knowledge of Khovanov homology or Lipshitz-Sarkar will be assumed.