[The Mathematical Atlas] [Search][Subject Index][MathMap][Tour][Help!]
[MathMap Icon]
ABOUT: [Introduction][History][Related areas][Subfields]
POINTERS: [Texts][Software][Web links][Selected topics here]

19: K-theory


Introduction

K-theory is an interesting blend of algebra and geometry. Originally defined for (vector bundles over) topological spaces it is now also defined for (modules over) rings, giving extra algebraic information about those objects.

History

Read Atiyah's, "K-Theory Past and Present" at here

Applications and related fields

Most of the geometric K-theory is treated with Algebraic Topology

See also 16E20, 18F25 [Schematic of subareas and related areas]

Subfields

K-Theory is the smallest of the 61 active areas of the MSC scheme: only 515 papers with primary classification 19-XX during 1980-1997. But the area 19-XX was only available as a primary classification for Math Reviews papers starting with MR96; hence the count above is an undercount of the true size of the field. (Even granting this, however, K-theory is a fairly small field.)

Browse all (old) classifications for this area at the AMS.


Textbooks, reference works, and tutorials

"Reviews in K-theory, 1940--84", edited by Bruce A. Magurn, American Mathematical Society, Providence, 1985, 811 pp., ISBN 0-8218-0088-4

Online chapters of a book-in-progress [Charles Weibel]

Software and tables

Other web sites with this focus

Selected topics at this site


You can reach this page through http://www.math-atlas.org/welcome.html
Last modified 2001/01/14 by Dave Rusin. Mail: