The Generating Family Spectrum of a Legendrian
The Generating Family Spectrum of a Legendrian
An important problem in contact topology is to define invariants for Legendrian submanifolds.听听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.听听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.听听I will also give some examples that demonstrate that the generating family spectrum is stronger than the generating family homology invariant. 听 This is joint work with Hiro Lee Tanaka.