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The Floer homotopy type of height functions on complex Grassmann manifolds


Author: David E. Hurtubise
Journal: Trans. Amer. Math. Soc. 349 (1997), 2493-2505
MSC (1991): Primary :, 55P15; Secondary 58B05, 58F09
MathSciNet review: 1401774
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Abstract: 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.


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Additional Information

David E. Hurtubise
Affiliation: Department of Mathematics, Occidental College, 1600 Campus Drive, Los Angeles, California 90041
Email: hurtubis@oxy.edu

DOI: https://doi.org/10.1090/S0002-9947-97-01848-5
Received by editor(s): January 29, 1996
Additional Notes: Research supported by an NSF graduate fellowship
Article copyright: © Copyright 1997 American Mathematical Society