Acylindrical hyperbolicity of the three-dimensional tame automorphism group
Lamy, Stéphane ; Przytycki, Piotr
HAL, hal-01885205 / Harvested from HAL
Text on HAL
We prove that the group STame($k^3$) of special tame automorphisms of the affine 3-space is not simple, over any base field of characteristic zero. Our proof is based on the study of the geometry of a 2-dimensional simply-connected simplicial complex C on which the tame automorphism group acts naturally. We prove that C is contractible and Gromov-hyperbolic, and we prove that Tame($k^3$) is acylindrically hyperbolic by finding explicit loxodromic weakly proper discontinuous elements.
Publié le : 2018-10-01
Classification:  [MATH.MATH-GR]Mathematics [math]/Group Theory [math.GR],  [MATH.MATH-GT]Mathematics [math]/Geometric Topology [math.GT] 
@article{hal-01885205,
     author = {Lamy, St\'ephane and Przytycki, Piotr},
     title = {Acylindrical hyperbolicity of the three-dimensional tame automorphism group},
     journal = {HAL},
     volume = {2018},
     number = {0},
     year = {2018},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-01885205}
}

Lamy, Stéphane; Przytycki, Piotr. Acylindrical hyperbolicity of the three-dimensional tame automorphism group. HAL, Tome 2018 (2018) no. 0, . http://gdmltest.u-ga.fr/item/hal-01885205/