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The Fibonacci automorphism of free Burnside groups

Ashot S. Pahlevanyan (2011)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd n 665 and even n = 16 k 8000 .

The Fibonacci automorphism of free Burnside groups

Ashot S. Pahlevanyan (2011)

RAIRO - Theoretical Informatics and Applications

We prove that the Fibonacci morphism is an automorphism of infinite order of free Burnside groups for all odd n 665 and even n = 16 k 8000 .

The rhombic dodecahedron and semisimple actions of Aut(Fₙ) on CAT(0) spaces

Martin R. Bridson (2011)

Fundamenta Mathematicae

We consider actions of automorphism groups of free groups by semisimple isometries on complete CAT(0) spaces. If n ≥ 4 then each of the Nielsen generators of Aut(Fₙ) has a fixed point. If n = 3 then either each of the Nielsen generators has a fixed point, or else they are hyperbolic and each Nielsen-generated ℤ⁴ ⊂ Aut(F₃) leaves invariant an isometrically embedded copy of Euclidean 3-space 𝔼³ ↪ X on which it acts as a discrete group of translations with the rhombic dodecahedron as a Dirichlet...

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