I will describe joint work with Abouzaid which constructs a stable homotopy theory refinement of Floer homology that has coefficients in the Morava K-theory spectra. The classifying spaces of finite groups satisfy Poincare duality for the Morava K-theories, which allows us to use this version of Floer homology to produce virtual fundamental chains for moduli spaces of Floer trajectories. As an application, we prove the Arnold conjecture for ordinary cohomology with coefficients in finite fields.
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- Geometry and Analysis Seminar