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SUMMARY:Equivariant Floer homotopy via Morse-Bott theory - Yusuf Baris  Ka
 rtal (University of Edinburgh)
DTSTART:20240614T150000Z
DTEND:20240614T153000Z
UID:TALK217798@talks.cam.ac.uk
DESCRIPTION:Morse theory provides an effective way to calculate the homolo
 gy of smooth manifolds\, in terms of critical points of a function and its
  gradient flow. Floer applied this idea in the infinite dimensional settin
 g to produce new invariants in symplectic and low dimensional topology\, a
 nd motivated by this\, Cohen\, Jones and Segal has shown how to obtain fin
 er information about the topology of a smooth manifold from the Morse theo
 ry\, thus providing a framework for refining Floer's invariant too. Howeve
 r\, neither Morse theory nor the framework of Cohen-Jones-Segal are compat
 ible with the compact group actions on the underlying manifold. In this ta
 lk\, I will explain joint work with Laurent Cote\, on how to define a new 
 framework for Morse-Bott functions in order to extract information about t
 he (Borel) equivariant stable homotopy type\, and how to use this in infin
 ite dimensions to construct equivariant Floer homotopy type. In the remain
 ing time\, I will report on the joint work in progress with Laurent Cote a
 nd Cheuk Yu Mak\, where we further incorporate derived manifolds into the 
 setup in order to understand genuine equivariant homotopy type and define 
 genuine equivariant Floer homotopy type.
LOCATION:External
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