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Symplectic Geometry Seminar

Equivariant, obstructed Morse homology

Erkao Bao (University of Minnesota)

Location:  Hill 705
Date & time: Thursday, 21 March 2024 at 1:15PM - 2:15PM

Abstract: In this talk, we define equivariant Morse homology for closed manifolds equipped with a finite group action. A significant challenge arises from the fact that the moduli spaces of trajectories of the negative gradient are usually not transversely cut out, a manifestation of the conflict between symmetry and genericity. We present two distinct approaches to tackle this issue:
Approach 1: stabilizing the Morse function;
Approach 2: obstruction bundle gluing in the spirit of semi-global Kuranishi structure.
The talk is based on joint works with Tyler Lawson and Ke Zhu.

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