Numerical invariants of contact manifolds and their divisors

Abstract: I will introduce an invariant E(K) of codim=2 contact submanifolds K of a contact manifold (of any dimension), generalizing the self-linking number SL(K) of transverse links in the contact 3-sphere. Extending the observation that SL(L)=1 mod 2 for knots, modular properties E(K) are intimately related to the divisibilities of certain Chern numbers. A generalization of Gompf's d3 invariant of contact 3-manifolds is also defined and used to uncover surprising properties of E(K). These tools provide novel information about Milnor numbers of complex hypersurface singularities.

mathematical physicsalgebraic topologydifferential geometryrepresentation theorystatistics theory

Audience: researchers in the topic

( slides | video )

Prague-Hradec Kralove seminar Cohomology in algebra, geometry, physics and statistics

Series comments: Virtual coffee starts on Zoom already 15 minutes before the seminar.