Stable modules and the D(2)-problem

Lecture notes series 301

F.E.A. Johnson

276 pages, parution le 22/10/2003

Ajouter à une liste

Indisponible

Résumé

This 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.

Introduction
Orders in semisimple algebras
Representation of finite groups
Stable modules and cancellation theorems
Relative homological algebra
The derived category of a finite group
k-invariants
Groups of periodic cohomology
Algebraic homotopy theory
Stability theorems
The D(2)-problem
Poincaré 3-complexes
Appendices
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	F.E.A. Johnson
Parution	22/10/2003
Nb. de pages	276
Format	15 x 22,7
Couverture	Broché
Poids	385g
Intérieur	Noir et Blanc
EAN13	9780521537490
ISBN13	978-0-521-53749-0