Equivariant Floer homotopy via Morse-Bott theory

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• Yusuf Baris Kartal (University of Edinburgh)
• Friday 14 June 2024, 16:00-16:30
• External.

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TRHW01 - Workshop on topology, representation theory and higher structures

Morse theory provides an effective way to calculate the homology of smooth manifolds, in terms of critical points of a function and its gradient flow. Floer applied this idea in the infinite dimensional setting to produce new invariants in symplectic and low dimensional topology, and motivated by this, Cohen, Jones and Segal has shown how to obtain finer information about the topology of a smooth manifold from the Morse theory, thus providing a framework for refining Floer’s invariant too. However, neither Morse theory nor the framework of Cohen-Jones-Segal are compatible with the compact group actions on the underlying manifold. In this talk, 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 the (Borel) equivariant stable homotopy type, and how to use this in infinite dimensions to construct equivariant Floer homotopy type. In the remaining time, I will report on the joint work in progress with Laurent Cote and 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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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