Michael Borinsky, Karen Vogtmann
Published 2023-01-03Version 1
The moduli space of rank $n$ graphs, the outer automorphism group of the free group of rank $n$ and Kontsevich's Lie graph complex have the same rational cohomology. We show that the associated Euler characteristic grows like $-e^{-1/4}\,(n/e)^n/(n\log n)^2$ as $n$ goes to infinity, and thereby prove that the total dimension of this cohomology grows rapidly with $n$.
The stable cohomology of automorphisms of free groups with coefficients in the homology representation
Integral Euler characteristic of Out F_{11}
First cohomology groups of the automorphism group of a free group with coefficients in the abelianization of the IA-automorphism group
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