Introduction to Algebraic K-Theory

by John Milnor

Overview

Algebraic K-theory describes a branch of algebra that centers about two functors. K0 and K1, which assign to each associative ring ∧ an abelian group K0∧ or K1∧ respectively. Professor Milnor sets out, in the present work, to define and study an analogous functor K2, also from associative rings to abelian groups. Just as functors K0 and K1 are important to geometric topologists, K2 is now considered to have similar topological applications. The exposition includes, besides K-theory, a considerable amount of related arithmetic.

Product Details

ISBN-13:	9780691081014
Publisher:	Princeton University Press
Publication date:	01/21/1972
Series:	Annals of Mathematics Studies , #72
Edition description:	New Edition
Pages:	200
Product dimensions:	5.90(w) x 8.90(h) x 0.60(d)

Table of Contents

• Frontmatter, pg. i
• Preface and Guide to the Literature, pg. vii
• Contents, pg. xiii
• §1. Projective Modules and K0Λ, pg. 1
• §2 . Constructing Projective Modules, pg. 19
• §3. The Whitehead Group K1Λ, pg. 25
• §4. The Exact Sequence Associated with an Ideal, pg. 33
• §5. Steinberg Groups and the Functor K2, pg. 39
• §6. Extending the Exact Sequences, pg. 53
• §7. The Case of a Commutative Banach Algebra, pg. 57
• §8. The Product K1Λ ⊗ K1Λ → K2Λ, pg. 63
• §9. Computations in the Steinberg Group, pg. 71
• §10. Computation of K2Z, pg. 81
• §11. Matsumoto’s Computation of K2 of a Field, pg. 93
• 12. Proof of Matsumoto’s Theorem, pg. 109
• §13. More about Dedekind Domains, pg. 123
• §14. The Transfer Homomorphism, pg. 137
• §15. Power Norm Residue Symbols, pg. 143
• §16. Number Fields, pg. 155
• Appendix. Continuous Steinberg Symbols, pg. 165
• Index, pg. 183

Editorial Reviews

John Milnor, Winner of the 2011 Abel Prize from the Norwegian Academy of Science and Letters

John Willard Milnor, Winner of the 2011 Leroy P. Steele Prize for Lifetime Achievement, American Mathematical Society

From the Publisher