Groups acting on graphs / Warren DICKS / Cambridge university press (1989)

Public ISBD Aucun avis sur cette notice. Faire une suggestion d'achat Titre : Groups acting on graphs Type de document : texte imprimé Auteurs : Warren DICKS, Auteur ; M.J. DUNWOODY, Auteur Editeur : Cambridge university press Année de publication : 1989 Collection : cambridge studies in advanced mathematics 17 Importance : 183 p. Format : 25 cm. ISBN/ISSN/EAN : 978-0-521-23033-9 Note générale : Index Langues : Anglais (eng) Langues originales : Anglais (eng) Catégories : MATHÉMATIQUES:Algébre Index. décimale : 04-03 Algébre Résumé : This is an advanced text and research monograph on groups acting on low-dimensional toplogical spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Here the treatment includes several of the standard results on groups acting on trees, as well as many original results on ends of groups and Boolean rings of graphs. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main Three-dimensional topics are the equivariant loop and sphere theorems. The prerequisites grow as the book progresses up the dimensions. A familiarity with group theory is sufficient background for at least the first third of the book, while the later chapters occasionally state without proof and then apply various facts normally found in one-year courses on homological algebra and algebraic topology. SOMMAIRE: Graphs of groups Trees for certain automorphism groups The exact sequence for a tree Free groups Free products The Boolean ring of a graph Distancetransitive graphs The Almost Stability Theorem Applications of the Almost Stability Theorem vii Poincare duality PDmodules PDgroups Subgroups of finite index Trees and Poincare duality Relative ends PD2pairs PD2groups Twodimensional complexes and threedimensional Simplifying surface maps The equivariant sphere and loop theorems The Loop Theorem Bibliography and author index Subject index Groups acting on graphs [texte imprimé] / Warren DICKS, Auteur ; M.J. DUNWOODY, Auteur . - Cambridge university press, 1989 . - 183 p. ; 25 cm.. - (cambridge studies in advanced mathematics 17) . ISBN : 978-0-521-23033-9 Index Langues : Anglais (eng) Langues originales : Anglais (eng) Catégories : MATHÉMATIQUES:Algébre Index. décimale : 04-03 Algébre Résumé : This is an advanced text and research monograph on groups acting on low-dimensional toplogical spaces, and for the most part the viewpoint is algebraic. Much of the book occurs at the one-dimensional level, where the topology becomes graph theory. Here the treatment includes several of the standard results on groups acting on trees, as well as many original results on ends of groups and Boolean rings of graphs. Two-dimensional topics include the characterization of Poincare duality groups and accessibility of almost finitely presented groups. The main Three-dimensional topics are the equivariant loop and sphere theorems. The prerequisites grow as the book progresses up the dimensions. A familiarity with group theory is sufficient background for at least the first third of the book, while the later chapters occasionally state without proof and then apply various facts normally found in one-year courses on homological algebra and algebraic topology. SOMMAIRE: Graphs of groups Trees for certain automorphism groups The exact sequence for a tree Free groups Free products The Boolean ring of a graph Distancetransitive graphs The Almost Stability Theorem Applications of the Almost Stability Theorem vii Poincare duality PDmodules PDgroups Subgroups of finite index Trees and Poincare duality Relative ends PD2pairs PD2groups Twodimensional complexes and threedimensional Simplifying surface maps The equivariant sphere and loop theorems The Loop Theorem Bibliography and author index Subject index

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