String topology and the configuration space of two points

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• Florian Naef (Trinity College Dublin)
• Wednesday 16 November 2022, 16:00-17:00
• MR13.

If you have a question about this talk, please contact Oscar Randal-Williams.

String topology is the study of operations on the homology of the free loop space LM for M a closed manifold. I will describe a model for (S^1-equivariant) string topology over the reals in terms of graph complexes. The construction comes together with an action of a graphical model for an approximation of the group of diffeomorphisms. From this we will be able to speculate how homotopy-invariant string topology is. Concretely, we will see that string topology is not invariant in families, by showing that \pi_) does not preserve the string coproduct and picks up an error term coming from a map \pi_(aut(M)) → H_ that vanishes on \pi_(Diff(M)). Finally, I will explain how this last part depends only on the configuration space of two points. This is based on joint work with T. Willwacher.

This talk is part of the Differential Geometry and Topology Seminar series.

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