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Large scale properties of groups; growth functions; Dehn functions; small cancellation properties; hyperbolicity and CAT(0); actions and representations; combinatorial group theory; presentations

13 votes

Is the Hurewicz theorem ever used to compute abelianizations?

The mapping class group of a smooth manifold $M$ is the group of all its self diffeomorphisms up to isotopy, i.e. $\pi_0(\operatorname{Diff}(M))\cong \pi_1(B\operatorname{Diff}(M))$. A large portion …
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