Groups Acting on Graphs

This 1989 monograph investigates groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic.

Warren Dicks (Author), M. J. Dunwoody (Author)

9780521230339, Cambridge University Press

Hardback, published 9 March 1989

300 pages
23.4 x 15.2 x 2.2 cm, 0.57 kg

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.

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.

Subject Areas: Groups & group theory [PBG]