Algebraic K-Theory and Its Applications

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Springer Science & Business Media, Jun 24, 1994 - Mathematics - 392 pages
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Algebraic K-Theory plays an important role in many areas of modern mathematics: most notably algebraic topology, number theory, and algebraic geometry, but even including operator theory. The broad range of these topics has tended to give the subject an aura of inapproachability. This book, based on a course at the University of Maryland in the fall of 1990, is intended to enable graduate students or mathematicians working in other areas not only to learn the basics of algebraic K-Theory, but also to get a feel for its many applications. The required prerequisites are only the standard one-year graduate algebra course and the standard introductory graduate course on algebraic and geometric topology. Many topics from algebraic topology, homological algebra, and algebraic number theory are developed as needed. The final chapter gives a concise introduction to cyclic homology and its interrelationship with K-Theory.
  

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Contents

I
1
II
7
III
11
IV
16
V
27
VI
32
VII
41
VIII
59
XXV
240
XXVI
245
XXVII
265
XXVIII
279
XXX
281
XXXI
289
XXXII
295
XXXIII
302

IX
62
X
74
XI
83
XII
92
XIII
108
XIV
132
XV
153
XVI
162
XVII
163
XVIII
168
XIX
187
XX
199
XXI
218
XXIII
221
XXIV
237
XXXIV
306
XXXV
325
XXXVI
331
XXXVII
332
XXXVIII
335
XXXIX
340
XL
350
XLII
355
XLIII
362
XLIV
369
XLV
371
XLVI
372
XLVII
377
XLVIII
383
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About the author (1994)

Jonathan Rosenberg is Assistant Professor of History at Hunter College of the City University of New York.

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