Stable modules and the D(2)-problem / F.E.A. Johnson.

By:

Johnson, F. E. A. (Francis Edward Anthony), 1946-

Material type: Text

TextSeries: London Mathematical Society lecture note series ; 301.Publication details: Cambridge, UK ; New York : Cambridge University Press, 2003.Description: 1 online resource (ix, 267 pages)Content type:

text

Media type:

computer

Carrier type:

online resource

ISBN:

9781107362284
1107362288

Subject(s): Genre/Form:

Electronic books.

Additional physical formats: Print version:: Stable modules and the D(2)-problem.DDC classification:

514/.2 22

LOC classification:

QA612.14 .J64 2003eb

Other classification:

31.61
SK 260
SK 280
MAT 553f
MAT 572f

Online resources:

Click here to access online

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.

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.

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Electronic-Books	OPJGU Sonepat- Campus	E-Books EBSCO			Available

Includes bibliographical references (pages 262-265) and index.

Print version record.

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.

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