Stable Modules and the D(2)-Problem: 301 (London Mathematical Society Lecture Note Series, Series Number 301) - Softcover

Johnson, F.E. A.

Softcover

ISBN 10: 0521537495 ISBN 13: 9780521537490

Publisher: Cambridge University Press, 2003

Synopsis

This 2003 book is concerned with two fundamental problems in low-dimensional topology. Firstly, the D(2)-problem, which asks whether cohomology detects dimension, and secondly the realization problem, which asks whether every algebraic 2-complex is geometrically realizable. The author shows that for a large class of fundamental groups these problems are equivalent. Moreover, in the case of finite groups, Professor Johnson develops general methods and gives complete solutions in a number of cases. In particular, he presents a complete treatment of Yoneda extension theory from the viewpoint of derived objects and proves that for groups of period four, two-dimensional homotopy types are parametrized by isomorphism classes of projective modules. 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.

About this title

Review

"This book is well-written, nicely organized, and is a pleasure to read." Mathematical Reviews, American Mathematical Society

Book Description

This 2003 book is concerned with two fundamental problems in low-dimensional topology. Professor Johnson develops general methods and gives complete solutions in a number of cases. It is ideal for graduate students wanting to learn low-dimensional homotopy theory as well as established researchers in the field.

Edition details

• Publisher: Cambridge University Press
• Publication date: 2003
• Language: English
• ISBN 10: 0521537495
• ISBN 13: 9780521537490
• Binding: Paperback
• Number of pages: 278