---

＜電子ブック＞
Homology of Linear Groups / by Kevin P. Knudson
(Progress in Mathematics. ISSN:2296505X ; 193)

版	1st ed. 2001.
出版者	Basel : Birkhäuser Basel : Imprint: Birkhäuser
出版年	2001
本文言語	英語
大きさ	XI, 192 p : online resource
冊子体	Homology of linear groups / Kevin P. Knudson ; : sz,: us
著者標目	*Knudson, Kevin P author SpringerLink (Online service)
件　名	LCSH:Algebraic topology FREE:Algebraic Topology
一般注記	1. 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 Daniel Quillen's definition of the higher algebraic K-groups of a ring emphasized the importance of computing the homology of groups of matrices. This text traces the development of this theory from Quillen's fundamental calculation of the cohomology of GLn (Fq). The stability theorems and low-dimensional results of A. Suslin, W. van der Kallen and others are presented as well as recent results for 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 should prove useful to graduate students and researchers in K-theory, group cohomology, algebraic geometry and topology Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-3-0348-8338-2

 類似資料