GT seminar: Higher torsion of Legendrians in one-jet space

Abstract: I'll introduce higher torsion from algebraic topology using the language of generating families for Legendrian submanifolds in standard contact one-jet spaces. I'll also propose a possible higher-dimensional generalization of rulings for such Legendrians. If the Legendrian is the lift of a nearby Lagrangian with such a ruling, then the torsion is trivial. (Although the torsion is non-trivial in general, any Legendrian which is the lift of a nearby Lagrangian and with non-trivial torsion would disprove the Nearby Lagrangian Conjecture.) This is joint work in progress with Dani Alvarez-Gavela and Kiyoshi Igusa.

This is a talk in our Geometry and Topology Seminar Series.