My question is the following:
In a paper I read that:
Any finite subgroup of $\mathrm{Aut}(F_n)$ can be realised as agroup of baspoint-preserving isometries of a graph of Euler characteristic $1-n$. Why is this fact true?
Thanks for help.
2026-03-28 21:34:21.1774733661
Why does every finite subgroup of $\mathrm{Aut}(F_n)$ acts on a graph of Euler characteristic $n-1$?
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This statement is called The Realization Theorem by Vogtmann in her survey paper. She gives the following references:
M. Culler, Finite groups of outer automorphisms of a free group, Contribu- tions to group theory, 197–207, Contemp. Math., 33, Amer. Math. Soc., Providence, R.I., 1984.
D. G. Khramtsov, Finite groups of automorphisms of free groups, Mat. Za- metki 38 (1985), no. 3, 386–392, 476.
B. Zimmermann, Uber Homomorphismen n-dimensionaler Henkelkörper und endliche Erweiterungen von Schottky-Gruppen, Comment. Math. Helv. 56 (1981), no. 3, 474–486.