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Article Dans Une Revue Journal de l'École polytechnique — Mathématiques Année : 2014

The tame automorphism group of an affine quadric threefold acting on a square complex

Résumé

We study the group Tame(SL$_2$) of tame automorphisms of a smooth affine 3-dimensional quadric, which we can view as the underlying variety of SL(2,$\mathbb{C}$). We construct a square complex on which the group admits a natural cocompact action, and we prove that the complex is CAT(0) and hyperbolic. We propose two applications of this construction: We show that any finite subgroup in Tame(SL$_2$) is linearizable, and that Tame(SL$_2$) satisfies the Tits alternative.

Dates et versions

hal-00949417 , version 1 (19-02-2014)

Identifiants

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Cinzia Bisi, Jean-Philippe Furter, Stéphane Lamy. The tame automorphism group of an affine quadric threefold acting on a square complex. Journal de l'École polytechnique — Mathématiques, 2014, 1, pp.161-223. ⟨hal-00949417⟩
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