Spectral sequences from Khovanov homology
Andrew Lobb (University of Durham)
Monday 12th October, 2015 16:00-17:00 Maths 522
Khovanov homology is an invariant of knots in the 3-sphere which turns out to be a first combinatorial approximation to many other, more analytically defined, invariants in low-dimensional topology. This is manifested by these latter invariants taking the form of the E_infinity pages of spectral sequences that have Khovanov homology as their E_2 pages. We shall discuss recent work (joint with John Baldwin and Matthew Hedden) explaining the ubiquity of these spectral sequences and giving universal proofs both of their invariance under Reidemeister moves and of their functoriality under knot cobordism. If there's time, we'll discuss some joint work with Raphael Zentner which concretely exploits these spectral sequences. No prior knowledge of Khovanov homology or of spectral sequences will be required.