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Conley index theory and condensed sets

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Yosuke Morita
Kyushu University
Mon, 19/06/2023 - 09:30 - 10:30
MPIM Lecture Hall

The Conley index is a spatial refinement of the Morse index. Informally speaking, it is a ‘space’ that describes the local dynamics around an isolated invariant subset of a topological dynamical system. In this talk, I will explain a new formulation of Conley index theory, which I think is simpler and more flexible than the traditional formulation. One important point is that the Conley index should be defined as a based equivariant condensed set/anima, not as a mere homotopy type of topological spaces. Beside that, our formulation features two classes of maps open embeddings and proper mapsof locally compact Hausdorff spaces, which makes us tempted to speculate that Conley index theory might be related to the six-functor formalism in some way.

The slides for the talk can be downloaded below.

File 202306Bonn.pdf10.06 MB
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