| Abstract:
A group is called \emph{tiny} if it cannot map onto the fundamental group of any aspherical $3$-manifold of negative Euler characteristic. For example,
knot groups are tiny. In this talk we show that if a finitely presented
tiny group $G$ maps onto the fundamental group of a compact aspherical
$3$-manifold $N$, then the simplicial volume of $N$ is bounded above in
terms of $G$. This is joint work with Ian Agol.
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