Joint IAS/PU Symplectic Geometry Seminar

An important problem in contact topology is to define invariants for Legendrian submanifolds. The rotation and Thurston-Bennequin numbers are classical integer invariants, and the last two decades have seen the development of non-classical invariants in the form of homology groups. For a Legendrian knot equipped with a generating family, Hiro Lee Tanaka and I have shown that the generating family homology groups have a stable homotopy refinement, the generating family spectrum. I will define this spectrum and show that when a Legendrian admits a generating family compatible Lagrangian filling, the generating family spectrum is equivalent to the suspension spectrum of the Lagrangian filling. I will also give some examples that demonstrate that the generating family spectrum is stronger than the generating family homology invariant. This is joint work with Hiro Lee Tanaka.