Geometry and Topology Seminar: Messing around with filtrations
15 December 2016 13:00 in CM221
Homological invariants in low-dimensional topology (like
Heegaard-Floer homology or Khovanov homology) often admit several
filtrations giving rise to numerical invariants that say something
directly about topology. If you take a couple of these filtrations and
blend them artfully, you can sometimes get much more information than
you expected. The first example of this is the so-called "upsilon"
invariant in Heegaard-Floer homology. Lukas Lewark and I came up a
while ago with an analogous invariant in quantum knot cohomologies, but
it's not yet written up. We decided to call it "gimel" but I can't
remember why. Anyways, I'll explain some of this story.