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Spaces of diffeomorphisms and embeddings of high-dimensional manifolds

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If you have a question about this talk, please contact Alexis Marchand .

Note unusual time

The homotopy type of the diffeomorphism group of a manifold is an object of great interest in algebraic and geometric topology. In this talk I will survey the “surgery-pseudoisotopy program” to study these objects for high-dimensional manifolds. In doing so, we will learn a bit about surgery theory, h-cobordisms and algebraic K-theory. We will end up deducing the computation of the rational homotopy groups of the diffeomorphism group of a disc in a range depending on its dimension.

If time permits (which I doubt), I will explain how the relative version of this program can be used to fully describe the homotopy type (localised away from 2) of spaces of long knots in high-dimensions up to a surprisingly big range.

This talk is part of the Junior Geometry Seminar series.

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