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### Periodic Floer homology

**Geometry/Topology**

Speaker: | Michael Hutchings, Stanford University |

Location: | 693 Kerr |

Start time: | Tue, Feb 20 2001, 2:10PM |

Given an area-preserving diffeomorphism of a surface, we define a chain complex, whose chains are generated by unions of periodic orbits, and whose differential counts certain pseudoholomorphic curves interpolating between them. We conjecture that the homology of this complex agrees with the Seiberg-Witten Floer homology of the mapping torus of the diffeomorphism. This is a joint project with Michael Thaddeus. There is some relation with the symplectic field theory of Eliashberg, Givental, and Hofer.