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OverviewThe text traces the homology theory of linear groups from the fundamental work of Quillen, Suslin, van der Kallen and others to recent results on rank one groups. A chapter on the Friedlander-Milnor-conjecture concerning the homology of algebraic groups made discrete is also included. This marks the first time that these results have been collected in a single volume. The book will be of interest to researchers and can be used as a textbook on graduate courses in K-theory and group cohomology. Full Product DetailsAuthor: Kevin P. KnudsonPublisher: Birkhauser Verlag AG Imprint: Birkhauser Verlag AG Edition: 2001 ed. Volume: 193 Dimensions: Width: 15.50cm , Height: 1.20cm , Length: 23.50cm Weight: 1.040kg ISBN: 9783764364151ISBN 10: 3764364157 Pages: 192 Publication Date: 01 December 2000 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of Contents1. Topological Methods.- 1.1. Finite Fields.- 1.2. Quillen’s Conjecture.- 1.3. Étale homotopy theory.- 1.4. Analytical Methods.- 1.5. Unstable Calculations.- 1.6. Congruence Subgroups.- Exercises.- 2. Stability.- 2.1. van der Kallen’s Theorem.- 2.2. Stability for rings with many units.- 2.3. Local rings and Milnor K-theory.- 2.4. Auxiliary stability results.- 2.5. Stability via Homotopy.- 2.6. The Rank Conjecture.- Exercises.- 3. Low-dimensional Results.- 3.1. Scissors Congruence.- 3.2. The Bloch Group.- 3.3. Extensions and Generalizations.- 3.4. Invariants of hyperbolic manifolds.- Exercises.- 4. Rank One Groups.- 4.1. SL2(?[1/p]).- 4.2. The Bruhat-Tits Tree.- 4.3. SL2(k[t]).- 4.4. SL2(k[t, t?1]).- 4.5. Curves of Higher Genus.- 4.6. Groups of Higher Rank.- Exercises.- 5. The Friedlander-Milnor Conjecture.- 5.1. Lie Groups.- 5.2. Groups over Algebraically Closed Fields.- 5.3. Rigidity.- 5.4. Stable Results.- 5.5. H1, H2, and H3.- Exercises.- Appendix A. Homology of Discrete Groups.- A.1. Basic Concepts.- A.2. Spectral Sequences.- B.1. Classifying Spaces.- Appendix C. Étale Cohomology.- C.1. Étale Morphisms and Henselian Rings.- C.2. Étale Cohomology.- C.3. Simplicial Schemes.ReviewsA book for graduates and researchers in K-theory, cohomology, algebraic geometry and topology. The theme is the development of the computing of the homology of the groups of matrices from Daniel Quillen's definitions of the higher algebraic K-groups. Stability theorems, low-dimensional results and the Friedlander-Milnor conjecture are discussed in this monograph. -Aslib Book Guide This marks the first time that many of these results have been collected in a single volume... -Mathematical Reviews A book for graduates and researchers in K-theory, cohomology, algebraic geometry and topology. The theme is the development of the computing of the homology of the groups of matrices from Daniel Quillen's definitions of the higher algebraic K-groups. Stability theorems, low-dimensional results and the Friedlander-Milnor conjecture are discussed in this monograph. --Aslib Book Guide This marks the first time that many of these results have been collected in a single volume! --Mathematical Reviews A book for graduates and researchers in K-theory, cohomology, algebraic geometry and topology. The theme is the development of the computing of the homology of the groups of matrices from Daniel Quillena (TM)s definitions of the higher algebraic K-groups. Stability theorems, low-dimensional results and the Friedlander-Milnor conjecture are discussed in this monograph. <p>a Aslib Book Guide <p> This marks the first time that many of these results have been collected in a single volumea ] <p>a Mathematical Reviews Author InformationTab Content 6Author Website:Countries AvailableAll regions |
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