1,722,117 research outputs found
Mélétios Syrigos, sa vie et ses œuvres
No full textPargoire Jules. Mélétios Syrigos, sa vie et ses œuvres. In: Échos d'Orient, tome 11, n°72, 1908. pp. 264-280
Mélétios Syrigos, sa vie et ses œuvres (fin)
No full textPargoire Jules. Mélétios Syrigos, sa vie et ses œuvres (fin). In: Échos d'Orient, tome 12, n°79, 1909. pp. 336-342
Mélétios Syrigos, sa vie et ses œuvres (suite)
No full textPargoire Jules. Mélétios Syrigos, sa vie et ses œuvres (suite). In: Échos d'Orient, tome 12, n°74, 1909. pp. 17-27
Stabiliser of an attractive fixed point of an IWIP automorphism of a free product
No full textFor a group of finite Kurosh rank and for some arbiratily free product decomposition of , , where is a finitely generated free group, we can associate some (relative) outer space . We define the relative boundary corresponding to the free product decomposition, as the set of infinite reduced words (with respect to free product length). By denoting the subgroup of which is consisted of the outer automorphisms which preserve the set of conjugacy classes of 's, we prove that for the stabiliser of an attractive fixed point in of an irreducible with irreducible powers automorphism relative to , it holds that it has a (normal) subgroup isomorphic to subgroup of such that is isomorphic to . The proof relies heavily on the machinery of the attractive lamination of an IWIP automorphism relative to
Asymmetry of outer space of a free product
No full textFor every free product decomposition of a group of finite Kurosh rank , where is a finitely generated free group, we can associate some (relative) outer space . We study the asymmetry of the Lipschitz metric on the (relative) Outer space . More specifically, we generalise the construction of Algom-Kfir and Bestvina, introducing an (asymmetric) Finsler norm that induces . Let's denote by the outer automorphisms of that preserve the set of conjugacy classes of 's. Then there is an -invariant function such that when is corrected by , the resulting norm is quasisymmetric. As an application, we prove that if we restrict to the -thick part of the relative Outer space for some \epsilon >0, is quasi-symmetric . Finally, we generalise for IWIP automorphisms of a free product a theorem of Handel and Mosher, which states that there is a uniform bound which depends only on the group, on the ratio of the relative expansion factors of any IWIP and its inverse. </p
Deformation spaces and irreducible automorphisms of a free product
No full textThe (outer) automorphism group of a finitely generated free group Fn, which we denote by Out(Fn), is a central object in the fields of geometric and combinatorial group theory. My thesis focuses on the study of the automorphism group of a free product of groups. As every finitely generated group can be written as a free product of finitely many freely indecomposable groups and a finitely generated free group (Grushko’s Theorem) it seems interesting to study the outer automorphism group of groups that split as a free product of simpler groups. Moreover, it turns out that many well known methods for the free case, can be used for the study of the outer automorphism group of such a free product. Recently, Out(Fn) is mainly studied via its action on a contractible space (which is called Culler - Vogtmann space or outer space and we denote it by CVn)and a natural asymmetric metric which is called the Lipschitz metric. More generally, similar objects exist for a general non-trivial free product. In particular, in this thesis we generalise theorems that are well known for CVn and Out(Fn) in the case of a finite free product, using the appropriate definitions and tools.Firstly, in [30], we generalise for an automorphism of a free product, a theorem due to Bestvina, Feighn and Handel, which states that the centraliser in Out(Fn) of an irreducible with irreducible powers automorphism of a free group is virtually infinite cyclic, where it is well known irreducible automorphisms form a (generic) class of automorphisms in the free case.In [31], we use the previous result in order to prove that the stabiliser of an attractive fixed point of an irreducible with irreducible powers automorphism in the relative boundary of a free product, can be computed. This was already well known for the free case and it is a result of Hilion.Finally, in [29] we prove that the Lipschitz metric for the general outer space is not even quasi-symmetric, but there is a ’nice’ function that bounds the asymmetry. As an application, we can see that this metric is quasi-symmetric if it is restricted on the thick part of outer space. The result in the free case is due to Algom-Kfir and Bestvina
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