The Euler characteristic of out \((F_n)\) (Q2227781)
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scientific article; zbMATH DE number 7310899
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Euler characteristic of out \((F_n)\) |
scientific article; zbMATH DE number 7310899 |
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The Euler characteristic of out \((F_n)\) (English)
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15 February 2021
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Summary: We prove that the rational Euler characteristic of Out \((F_n)\) is always negative and its asymptotic growth rate is \(\Gamma (n - \frac{3}{2}) / \sqrt{2 \pi} \log^2n\). 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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automorphisms of free groups
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Euler characteristic
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asymptotic expansions
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