Topology Seminar (Introductory Talk): Morse-Bott cohomology of flow categories

Seminar | September 27 | 2-3 p.m. | 740 Evans Hall

 Zhengyi Zhou, University of California, Berkeley

 Department of Mathematics

Flow category was introduced by Cohen, Jones and Segal to organize all the moduli spaces in Floer-type cohomology theories. In this talk, I will review three constructions of the cohomology on flow categories in the Morse-Bott case, namely the Austin-Braam's model, the Fukaya's model and the cascades model. I will explain how homological perturbation theory can help solving the transversality challenges in the Austin-Braam's model and how the cascades model can be viewed as applying the homological perturbation lemma to the Austin-Braams's model.