Event Type:

Geometry-Topology Seminar

Date/Time:

Monday, January 29, 2018 - 13:00 to 14:00

Location:

Stag 162

Guest Speaker:

Dev Sinha

Institution:

University of Oregon

Abstract:

A wonderful theorem of Hilton and Milnor implies that the rational homotopy groups of a wedge of spheres is a free Lie algebra. But given two maps from a sphere to a wedge of spheres, how could we tell whether or not they were homotopic module torsion? That is, what theory plays the role for homotopy that cohomology does for homology? I will describe linking (also known as Hopf) invariants, developed in work with Ben Walter, which do the trick, not just for wedges of spheres but for any simply connected space. While there is much to be said about Koszul duality, I will focus on drawing pictures. The theory for the fundamental group has yet to be developed, and I will say a few words about that.