CBMS Regional Conference Series in Mathematics 1974; 68 pp; softcover Number: 20 Reprint/Revision History: fifth printing 2000 ISBN10: 0821816705 ISBN13: 9780821816707 List Price: US$28 Member Price: US$22.40 All Individuals: US$22.40 Order Code: CBMS/20
 Table of Contents Part I. Introduction  Elementary matrices
 Stability
 \(K_1(A[t])\) and unipotents
 Grothendieck and Whitehead groups of categories with exact sequences
 A Grothendieck style definition of \(K_1(A)\)
 Homology, mapping cones, and Euler characteristics
 Resolution theorems
 Projective resolutions and regular rings
 Hilbert's syzygy theorem
 Appendix 1
Part II. Localisation, divissage and applications  The localisation sequence
 Categories of nilpotent endomorphisms
 \(K_1(A[t,t^1])\)
 Devissage
 Some calculations with the localisation sequence and \(K_1\)Laurent theorem
 Computations with the MayerVietoris sequence
 References
