Floer homotopy theory and Morava Ktheory
Floer homotopy theory and Morava Ktheory

Andrew J. Blumberg, Columbia University
Zoom link: https://princeton.zoom.us/j/96282936122
Passcode: 998749
I will describe joint work with Abouzaid which constructs a stable homotopy theory refinement of Floer homology that has coefficients in the Morava Ktheory spectra. The classifying spaces of finite groups satisfy Poincare duality for the Morava Ktheories, 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.