The Generating Family Spectrum of a Legendrian

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Lisa Traynor, Bryn Mawr College
Fine Hall 110

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.