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Algebraic Topology and Physics Seminar, Week 6

Algebraic Topology and Physics Seminar Week 6: Max Lipiansky, "Semi-Infinite Cycles in Floer Theory"

Title: Semi-Infinite Cycles in Floer Theory
Speaker: Max Lipiansky, Columbia University
Date: Tuesday, February 28, 2012
Time: 10:30am – 12:00pm
Place: Seminar Room 313, Simons Center








Floer theory associates a Morse-type chain complex to certain infinite dimensional configuration spaces equipped with a functional. We will describe an alternative formulation that may be viewed as a version of geometric homology for semi-infinite cycles. Our approach allows one to bypass many of the technical transversality and gluing arguments that are necessary to set up the Morse theory. This is particularly useful in various equivariant formulations where transversality issues are not always resolved. In addition, our approach allows one to introduce refined Floer invariants such as Floer bordism which are inaccessible by Morse-theoretic methods.