Stable modules and the D(2)-problem /

Stable modules and the D(2)-problem /

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Bibliographic Details
Author / Creator:	Johnson, F. E. A. (Francis Edward Anthony), 1946-
Imprint:	Cambridge, UK ; New York : Cambridge University Press, 2003.
Description:	1 online resource (ix, 267 pages).
Language:	English
Series:	London Mathematical Society lecture note series ; 301 London Mathematical Society lecture note series ; 301.
Subject:	Low-dimensional topology. Homotopy theory. Group algebras. Group algebras. Homotopy theory. Low-dimensional topology. Electronic books.
Format:	E-Resource Book
URL for this record:	http://pi.lib.uchicago.edu/1001/cat/bib/11181013

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ISBN:	9781107362284 1107362288 0521537495 9780521537490
Notes:	Includes bibliographical references (pages 262-265) and index. Print version record.
Summary:	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.
Other form:	Print version: Johnson, F.E.A. (Francis Edward Anthony), 1946- Stable modules and the D(2)-problem. Cambridge, UK ; New York : Cambridge University Press, 2003 0521537495

Table of Contents:

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. Poincare
3 complexes.