The Euler characteristic of Out()

  • Michael Borinsky

    National Institute for Subatomic Physics, Amsterdam, Netherlands
  • Karen Vogtmann

    University of Warwick, Coventry, UK
The Euler characteristic of Out($F_n$) cover
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We prove that the rational Euler characteristic of Out() is always negative and its asymptotic growth rate is . This settles a 1987 conjecture of J. Smillie and the second author. We establish connections with the Lambert -function and the zeta function.

Cite this article

Michael Borinsky, Karen Vogtmann, The Euler characteristic of Out(). Comment. Math. Helv. 95 (2020), no. 4, pp. 703–748

DOI 10.4171/CMH/501