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Prospects for Floer homotopy theory

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  • UserMohammed Abouzaid, Columbia
  • ClockWednesday 01 February 2017, 16:00-17:00
  • HouseMR13.

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The last twenty years have seen tremendous developments in symplectic and contact topology, both in the development of Floer theoretic invariants (pseudo-holomorphic curve) that establish rigidity phenomena, and in a new wave of h-principles that achieve long-sought flexible constructions. This has led Eliashberg to advocate that it should be possible to implement any construction not forbidden by Floer theory, further stressing the problem of understanding what invariant information can be extracted from the moduli spaces of holomorphic curves. In this lecture, I will begin by giving an introduction to Floer theory and its applications in symplectic topology, before sketching a conjectural picture, developed jointly with Blumberg and Kragh, for a homotopical refinement which extends the original ideas of Cohen, Jones, and Segal.

This talk is part of the Differential Geometry and Topology Seminar series.

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