Nordic Topology Meeting 
Thursday, August 27, 12:05 - 12:50

Thomas Kragh: Simple homotopy type of exact Lagrangians.

Previous work by Abouzaid and me (building on work by Fukaya, Seidel, Smith, Nadler, Viterbo + more) shows that closed exact Lagrangians in cotangent bundles are homotopic to the zero section. In this talk I will sketch a proof (by Abouzaid and me) of the new result that the map to the zero-section is in fact a simple homotopy equivalence.

I will begin by reviewing what simple homotopy type is, and how this relates to Morse theory. Then I will define exact Lagrangians, and review Lagrangian intersection Floer homology with local coefficients, and some of the geometry behind this. I will then sketch how a specific deformation of any exact Lagrangian L provides a convenient action filtration on Floer homology, which induces a Serre-type spectral sequence converging to the Floer homology. This spectral sequence holds the key to proving simple homotopy type.