arXiv math/05022482005-02math.GR

A Fixed Point Theorem for Deformation Spaces of G-trees

Matt Clay

备注：: 5 pages shorter than original, Section 3 and Proposition 4.4 are now replaced by citing a Theorem of Dunwoody-Roller (Theorem 3.1). To appear in Commentarii Mathematici Helvetici. Previous title: A Generalization of Culler's Theorem

英文摘要：

For a finitely generated free group F_n, of rank at least 2, any finite subgroup of Out(F_n) can be realized as a group of automorphisms of a graph with fundamental group F_n. This result, known as Out(F_n) realization, was proved by Zimmermann, Culler and Khramtsov. This theorem is comparable to Nielsen realization as proved by Kerckhoff: for a closed surface with negative Euler characteristic, any finite subgroup of the mapping class group can be realized as a group of isometries of a hyperbolic surface. Both of these theorems have restatements in terms of fixed points of actions on spaces naturally associated to them. For a nonnegative integer n we define a class of groups (GVP(n)) and prove a similar statement for their outer automorphism groups.

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