Topology Seminar

This is joint work with Lisa Traynor. I'll introduce the notion of generating families, which produce many interesting examples of Legendrians in jet bundles (for example, Legendrian knots in R^3). Then I'll introduce an invariant of generating families, called generating family spectra, which lift classically known (co)homological invariants. I'll present a proof that there are infinitely many connected components of generating families that can be detected using spectra that cannot be detected classically -- so generating family spectra are stronger invariants than previously known invariants. If time allows, I may explain how generating families form an infinity-category enriched in spectra, and the invariants in this talk are (dual to) the endomorphisms -- so, in particular, admit a (co)multiplication.