A family of Floer functions on the infinite dimensional complex Grassmann manifold is defined by taking direct limits of height functions on adjoint orbits of unitary groups. The Floer cohomology of a generic function in the family is computed using the Schubert calculus. The Floer homotopy type of this function is computed and the Floer cohomology which was computed algebraically is recovered from the Floer homotopy type. Certain non-generic elements of this family of Floer functions were shown to be related to the symplectic action functional on the universal cover of the loop space of a finite dimensional complex Grassmann manifold in the author's preprint The Floer homotopy type of complex Grassmann manifolds.
All Science Journal Classification (ASJC) codes
- Applied Mathematics