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Hiro Lee Tanaka, PMA 12.166: Stable homotopy invariants from generating families
Monday, February 03, 2025, 02:00am - 03:00am
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.
Location: PMA 12.166

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