Dimension of the Torelli group for Out(Fn)

By M. Bestvina, Kai-Uwe Bux, Dany Margalit. 2006

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Let $\mathcal{T}_{n}$ be the kernel of the natural map Out(Fn)→GLn(ℤ). We use combinatorial Morse theory to prove that $\mathcal{T}_{n}$ has an Eilenberg–MacLane space which is (2n-4)-dimensional and that $H_{2n-4}(\mathcal{T}_{n},\mathbb{Z})$ is not finitely generated (n≥3). In particular, this shows that the cohomological dimension of $\mathcal{T}_{n}$ is equal to 2n-4 and recovers the result of Krstić–McCool that $\mathcal{T}_3$ is not finitely presented. We also give a new proof of the fact, due to Magnus, that $\mathcal{T}_{n}$ is finitely generated.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/55ee2fbcad39b2a426f8c1aba5fa5ddcfb877e66

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