Topology Seminar (Main Talk): Morse-Bott cohomology from homological perturbation

Seminar | September 27 | 4-5 p.m. | 3 Evans Hall

 Zhengyi Zhou, University of California, Berkeley

 Department of Mathematics

In this talk, I will give a new construction of the cochain complexes for flow categories in the Morse-Bott case, where the underlying vector space is generated by the cohomology of the 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 structure of the flow category. I will then discuss the equivariant counterpart and the generalization in the polyfold theory.