A Course in Homological Algebra

✍ Scribed by Peter J. Hilton, Urs Stammbach (auth.)

• Publisher: Springer-Verlag New York
• Year: 1997
• Tongue: English
• Leaves: 375
• Series: Graduate Texts in Mathematics 4
• Edition: 2
• Category: Library

✦ Synopsis

We have inserted, in this edition, an extra chapter (Chapter X) entitled "Some Applications and Recent Developments." The first section of this chapter describes how homological algebra arose by abstraction from algebraic topology and how it has contributed to the knowledge of topology. The other four sections describe applications of the methods and results of homological algebra to other parts of algebra. Most of the material presented in these four sections was not available when this text was first published. Naturally, the treatments in these five sections are somewhat cursory, the intention being to give the flavor of the homo­ logical methods rather than the details of the arguments and results. We would like to express our appreciation of help received in writing Chapter X; in particular, to Ross Geoghegan and Peter Kropholler (Section 3), and to Jacques Thevenaz (Sections 4 and 5). The only other changes consist of the correction of small errors and, of course, the enlargement of the Index. Peter Hilton Binghamton, New York, USA Urs Stammbach Zurich, Switzerland Contents Preface to the Second Edition vii Introduction. . I. Modules.

✦ Table of Contents

Front Matter....Pages i-xii
Introduction....Pages 1-9
Modules....Pages 10-39
Categories and Functors....Pages 40-83
Extensions of Modules....Pages 84-115
Derived Functors....Pages 116-165
The Künneth Formula....Pages 166-183
Cohomology of Groups....Pages 184-228
Cohomology of Lie Algebras....Pages 229-254
Exact Couples and Spectral Sequences....Pages 255-305
Satellites and Homology....Pages 306-330
Some Applications and Recent Developments....Pages 331-355
Back Matter....Pages 357-366

✦ Subjects

K-Theory