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Geometric Analysis Seminar

Morse-Bott cohomology from homological perturbation theory

Zhengyi Zhou (IAS)

Location:  Room 705
Date & time: Tuesday, 07 May 2019 at 2:10PM - 3:10PM

Abstract: In this talk, I will explain the following phenomenon in Morse-Bott constructions in Floer theories: formal application of homological perturbation lemma tends to give well-defined constructions with weaker transversality requirements. In particular, I will explain why the cascades construction can be viewed as an application of such principle. Then I will give a new construction of the Morse-Bott cochain complex, where the underlying vector space is generated by the cohomology of critical manifolds. This new construction has two nice features: (1) It requires the minimum amount of transversality. (2) The choices made in the construction do not depend on the moduli spaces.

Time permitting, I will discuss the equivariant counterpart and the generalization in the polyfold theory.

This will be a joint seminar with Geometry/Topology Seminar