Description

Book Synopsis
Originally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological 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. 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 which require knowledge of homological algebra and algebraic topology. This book is essential reading for anyone contemplating working in the subject.

Table of Contents
Preface; Conventions; 1. Groups and graphs; 2. Cutting graphs and building trees; 3. The almost stability theorem; 4. Applications of the almost stability theorem; 5. Poincaré duality; 6. Two-dimensional complexes and three-dimensional manifolds; Bibliography and author index; Symbol index; Subject index.

Groups Acting on Graphs 17 Cambridge Studies in Advanced Mathematics Series Number 17

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    A Paperback by Warren Dicks, M. J. Dunwoody

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      Book details

      Publisher Cambridge University Press
      Published 4/14/2011 12:00:00 AM
      ISBN-13 9780521180009
      978-0521180009
      ISBN-10 0521180007
      Also in:
      Groups and group theory

      Description

      Book Synopsis
      Originally published in 1989, this is an advanced text and research monograph on groups acting on low-dimensional topological 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. 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 which require knowledge of homological algebra and algebraic topology. This book is essential reading for anyone contemplating working in the subject.

      Table of Contents
      Preface; Conventions; 1. Groups and graphs; 2. Cutting graphs and building trees; 3. The almost stability theorem; 4. Applications of the almost stability theorem; 5. Poincaré duality; 6. Two-dimensional complexes and three-dimensional manifolds; Bibliography and author index; Symbol index; Subject index.

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