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SUMMARY:$G_2$-manifolds and their moduli spaces - Sebastian  Goette (Unive
 rsität Freiburg)
DTSTART:20240614T101500Z
DTEND:20240614T111500Z
UID:TALK217357@talks.cam.ac.uk
DESCRIPTION:In the first part of the talk\, I will introduce closed Rieman
 nian manifolds with holonomy $G_2$ ($G_2$-manifolds for short). I will sum
 marise 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 i
 n general neither connected nor aspherical\, otherwise\, little is known.\
 nIn the second half\, I will introduce calibrated submanifolds of $G_2$-ma
 nifolds (associative and coassociative submanifolds). I will then introduc
 e a very crude topological approximation and speculate about the space of 
 these so-called homotopy associatives.
LOCATION:External
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