Groups Acting on Graphs: 17 (Cambridge Studies in Advanced Mathematics, Series Number 17) - Hardcover

Dicks, Warren; Dunwoody, M. J.

Hardcover

ISBN 10: 0521230330 ISBN 13: 9780521230339

Publisher: Cambridge University Press, 1989

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.

About this title

Book Description

This 1989 monograph investigates groups acting on low-dimensional topological spaces, and for the most part the viewpoint is algebraic. A familiarity with group theory is sufficient background for 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.

Synopsis

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. 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. Since almost all the material is appearing here in the book form for the first time, and much is appearing in print for the first time, this book is essential reading for anyone contemplating working in the subject.

Edition details

• Publisher: Cambridge University Press
• Publication date: 1989
• Language: English
• ISBN 10: 0521230330
• ISBN 13: 9780521230339
• Binding: Hardcover
• Number of pages: 300