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Titlebook: Homology of Linear Groups; Kevin P. Knudson Book 2001 Birkhäuser Verlag 2001 Cohomology.Homotopy.K-theory.algebra.cohomology of groups.hom

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书目名称Homology of Linear Groups
编辑Kevin P. Knudson
视频video
丛书名称Progress in Mathematics
图书封面Titlebook: Homology of Linear Groups;  Kevin P. Knudson Book 2001 Birkhäuser Verlag 2001 Cohomology.Homotopy.K-theory.algebra.cohomology of groups.hom
描述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.
出版日期Book 2001
关键词Cohomology; Homotopy; K-theory; algebra; cohomology of groups; homology; homotopy theory
版次1
doihttps://doi.org/10.1007/978-3-0348-8338-2
isbn_softcover978-3-0348-9523-1
isbn_ebook978-3-0348-8338-2Series ISSN 0743-1643 Series E-ISSN 2296-505X
issn_series 0743-1643
copyrightBirkhäuser Verlag 2001
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Stability,at the map .is an isomorphism for . ≥ .(.)? The answer is certainly no if for example . is the free abelian group of rank ., but there are many examples for which stability does happen. For example, there are stability results for the sequenceof symmetric groups [.] and also for the mapping class gr
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Low-dimensional Results, .(.(.),ℤ) ≅ .(.(.),ℤ) for . local with infinite residue field. Thus, one need only consider the former group. In this case, Suslin completely described the structure of .(.(.),ℤ) —it surjects onto the second Milnor .-group . (.) and the kernel of this map is the image of .(.(.),ℤ).
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Rank One Groups,known tiling of the hyperbolic plane by .(ℤ)-translates of an ideal triangle (see, e.g. [.], p. 215) and there is the Bruhat-Tits tree associated to a field with discrete valuation. Often, the action implies something about the structure of the group such as the existence of an amalgamated free prod
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Progress in Mathematicshttp://image.papertrans.cn/h/image/428151.jpg
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978-3-0348-9523-1Birkhäuser Verlag 2001
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发表于 2025-3-23 06:49:25 | 显示全部楼层
Low-dimensional Results, .(.(.),ℤ) ≅ .(.(.),ℤ) for . local with infinite residue field. Thus, one need only consider the former group. In this case, Suslin completely described the structure of .(.(.),ℤ) —it surjects onto the second Milnor .-group . (.) and the kernel of this map is the image of .(.(.),ℤ).
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