### 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.

Original language | English (US) |
---|---|

Pages (from-to) | 2493-2505 |

Number of pages | 13 |

Journal | Transactions of the American Mathematical Society |

Volume | 349 |

Issue number | 6 |

State | Published - 1997 |

### Fingerprint

### All Science Journal Classification (ASJC) codes

- Mathematics(all)
- Applied Mathematics

### Cite this

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*Transactions of the American Mathematical Society*, vol. 349, no. 6, pp. 2493-2505.

**The floer homotopy type of height functions on complex grassmann manifolds.** / Hurtubise, David Edward.

Research output: Contribution to journal › Article

TY - JOUR

T1 - The floer homotopy type of height functions on complex grassmann manifolds

AU - Hurtubise, David Edward

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=21744432603&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=21744432603&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:21744432603

VL - 349

SP - 2493

EP - 2505

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

SN - 0002-9947

IS - 6

ER -