Author | Knudson, Kevin P. author |
---|---|
Title | Homology of Linear Groups [electronic resource] / by Kevin P. Knudson |
Imprint | Basel : Birkhรคuser Basel : Imprint: Birkhรคuser, 2001 |
Connect to | http://dx.doi.org/10.1007/978-3-0348-8338-2 |
Descript | XI, 192 p. online resource |
1. Topological Methods -- 1.1. Finite Fields -- 1.2. Quillenโs Conjecture -- 1.3. รtale homotopy theory -- 1.4. Analytical Methods -- 1.5. Unstable Calculations -- 1.6. Congruence Subgroups -- Exercises -- 2. Stability -- 2.1. van der Kallenโs 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. รtale Cohomology -- C.1. รtale Morphisms and Henselian Rings -- C.2. รtale Cohomology -- C.3. Simplicial Schemes