$G_2$-manifolds and their moduli spaces

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• Sebastian Goette (Universität Freiburg)
• Friday 14 June 2024, 11:15-12:15
• External.

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TRHW01 - Workshop on topology, representation theory and higher structures

In the first part of the talk, I will introduce closed Riemannian manifolds with holonomy $G_2$ ($G_2$-manifolds for short). I will summarise some known results about the topology of $G_2$-manifolds and their moduli spaces. By results of Joyce, the moduli space of $G_2$-metrics on a given 7-manifold $M$ is a smooth manifold of dimension $b_3(M)$. It is in general neither connected nor aspherical, otherwise, little is known. In the second half, I will introduce calibrated submanifolds of $G_2$-manifolds (associative and coassociative submanifolds). I will then introduce a very crude topological approximation and speculate about the space of these so-called homotopy associatives.

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

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