The Euler characteristic of Out()
Michael Borinsky
National Institute for Subatomic Physics, Amsterdam, NetherlandsKaren Vogtmann
University of Warwick, Coventry, UK
![The Euler characteristic of Out($F_n$) cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserials%2Fcover-cmh.png&w=3840&q=90)
Abstract
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