Groups Acting on Graphs

Erscheinungsjahr 2003
ISBN: 978-0-521-23033-9
Verlag: Cambridge University Press

Buch, Englisch, Band 17, 304 Seiten, Format (B × H): 157 mm x 235 mm, Gewicht: 640 g

Reihe: Cambridge Studies in Advanced Mathematics

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.

Autoren/Hrsg.

Dicks, Warren

Dunwoody, M. J.

Bollobas, Bela

Fachgebiete

• Mathematik | Informatik Mathematik Operations Research Graphentheorie
• Mathematik | Informatik Mathematik Algebra Algebraische Strukturen, Gruppentheorie

Inhaltsverzeichnis

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.