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OverviewThis 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. Full Product DetailsAuthor: F. E. A. Johnson (University College London)Publisher: Cambridge University Press Imprint: Cambridge University Press (Virtual Publishing) Volume: 301 ISBN: 9780511550256ISBN 10: 0511550251 Publication Date: 04 August 2010 Audience: Professional and scholarly , Professional & Vocational Format: Undefined Publisher's Status: Active Availability: In stock  We have confirmation that this item is in stock with the supplier. It will be ordered in for you and dispatched immediately. Table of Contents1. 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. Poincaré 3-complexes.ReviewsThis book is well-written, nicely organized, and is a pleasure to read. Mathematical Reviews, American Mathematical Society Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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