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arXiv · 1802.00481

Presqu'un immeuble pour le groupe des automorphismes modérés

Stéphane Lamy·Piotr Przytycki
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Abstract

Inspired by the Bruhat-Tits building of SL$_n$($\mathbb Q_p$), we construct a complete metric space X with an action of the tame automorphism group of the affine space Tame($K^n$). The points in X are certain monomial valuations, and X admits a natural structure of Euclidean CW-complex of dimension n-1. When n = 3, and for K of characteristic zero, we prove that X has non-positive curvature and is simply connected, hence is a CAT(0) space. As an application we obtain the linearizability of finite subgroups in Tame($K^3$).

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Stéphane Lamy, Piotr Przytycki. 2019-10-09. Presqu'un immeuble pour le groupe des automorphismes modérés. https://doi.org/10.5802/ahl.83

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