Stable Modules and the D(2)-Problem [Paperback]

This 2003 book deals with two fundamental problems in low-dimensional topology with an eye on wider context.This book is concerned with two fundamental problems in low dimensional topology, the D(2)-problem and the realization problem. Professor Johnson develops general methods and gives complete solutions in a number of cases. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.This book is concerned with two fundamental problems in low dimensional topology, the D(2)-problem and the realization problem. Professor Johnson develops general methods and gives complete solutions in a number of cases. This book is carefully written with an eye on the wider context and as such is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.Concerned with two fundamental problems in low-dimensional topology, the D(2)-problem and the realization problem, F.E.A. Johnson develops general methods and provides complete solutions in some instances. His book is suitable for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.1. Orders in semisimple algebras; 2. Representation of finite groups; 3. Stable modules and cancellation theorems; 4. Relative homological algebra; 5. The derived category of a finite group; 6. k-invariants; 7. Groups of periodic cohomology; 8. Algebraic homotopy theory; 9. Stability theorems; 10. The D(2)-problem; 11. Poincar? 3-complexes. This book is well-written, nicely organized, and is a pleasure to read. Mathematical Reviews, American Mathematical Society