Floer homotopy without spectra
Mohammed Abouzaid (Columbia)
Abstract: The construction of Cohen-Jones-Segal of Floer homotopy types associated to appropriately oriented flow categories extracts from the morphisms of such a category the data required to assemble an iterated extension of free modules (in an appropriate category of spectra). I will explain a direct (geometric) way for defining the Floer homotopy groups which completely bypasses stable homotopy theory. The key point is to work on the geometric topology side of the Pontryagin-Thom construction. Time permitting, I will also explain joint work in progress with Blumberg for building a spectrum from the new point of view, as well as various generalisations which are relevant to Floer theory.
algebraic geometrydifferential geometrygeometric topologysymplectic geometry
Audience: researchers in the topic
Series comments: This is the free mathematics seminar. Free as in freedom. We use only free and open source software to run the seminar.
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| Organizers: | Jonny Evans*, Ailsa Keating, Yanki Lekili* |
| *contact for this listing |