The Floer homotopy type of height functions on complex Grassmann manifolds. (English) Zbl 0907.55009
Along the line of the work of Cohen, Jones, and Segal on the Floer homotopy type, the author provides a concrete example over the infinite complex Grassmannian. The paper considers a family of Floer functions obtained as direct limits of height functions on adjoint orbits of unitary groups. It is shown that the relative index of any two critical points is finite, and that the functions satisfy the Morse-Bott condition. Through an explicit description of the gradient flow lines in terms of Schubert cells, the flow category is introduced and the corresponding Floer homotopy type is constructed.
Reviewer: Matilde Marcolli (Cambridge / Mass.)
MSC:
| 55P15 | Classification of homotopy type |
| 58B05 | Homotopy and topological questions for infinite-dimensional manifolds |
| 37D15 | Morse-Smale systems |
Keywords:
Floer homotopy typeReferences:
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