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Título: Relative hyperbolicity of graphs of free groups with cyclic edge groups
Autores: Richer, Émilie.
Fecha: 2006
Publicador: McGill University
Fuente: Ver documento
Tipo: Electronic Thesis or Dissertation
Tema: Hyperboloid.
Free groups.
Descripción: We prove that any finitely generated group which splits as a graph of free groups with cyclic edge groups is hyperbolic relative to certain finitely generated subgroups, known as the peripheral subgroups. Each peripheral subgroup splits as a graph of cyclic groups. Any graph of free groups with cyclic edge groups is the fundamental group of a graph of spaces X where vertex spaces are graphs, edge spaces are cylinders and attaching maps are immersions. We approach our theorem geometrically using this graph of spaces.
We apply a "coning-off" process to peripheral subgroups of the universal cover X̃ → X obtaining a space Cone(X̃) in order to prove that Cone (X̃) has a linear isoperimetric function and hence satisfies weak relative hyperbolicity with respect to peripheral subgroups.
We then use a recent characterisation of relative hyperbolicity presented by D.V. Osin to serve as a bridge between our linear isoperimetric function for Cone(X̃) and a complete proof of relative hyperbolicity. This characterisation allows us to utilise geometric properties of X in order to show that pi1( X) has a linear relative isoperimetric function. This property is known to be equivalent to relative hyperbolicity.
Keywords. Relative hyperbolicity; Graphs of free groups with cyclic edge groups, Relative isoperimetric function, Weak relative hyperbolicity.
Idioma: en