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The Euler characteristic of $\operatorname{Out}(F_n)$

· 2019 · math.GR · arXiv 1907.03543

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abstract

We prove that the rational Euler characteristic of $\operatorname{Out}(F_n)$ is always negative and its asymptotic growth rate is $\Gamma(n- \frac32)/\sqrt{2\pi} \log^2 n$. This settles a 1987 conjecture of J. Smillie and the second author. We establish connections with the Lambert $W$-function and the zeta function.

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math.GR 1

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2019 1

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CONDITIONAL 1

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On the top-dimensional $\ell^2$-Betti numbers

math.GR · 2019-09-04 · conditional · novelty 7.0

A transfer trick yields non-vanishing top ℓ2-Betti numbers for Out(Fn), Aut(Fn) and Torelli groups, vanishing results for subgroups of 3-manifold groups, and ergodic dimension d+1 for F2^d × Z.

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  • On the top-dimensional $\ell^2$-Betti numbers math.GR · 2019-09-04 · conditional · none · ref 12 · internal anchor

    A transfer trick yields non-vanishing top ℓ2-Betti numbers for Out(Fn), Aut(Fn) and Torelli groups, vanishing results for subgroups of 3-manifold groups, and ergodic dimension d+1 for F2^d × Z.