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Homotopy Theory of C*-Algebras / by Paul Arne Østvær
(Frontiers in Mathematics. ISSN:16608054)
版 | 1st ed. 2010. |
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出版者 | (Basel : Springer Basel : Imprint: Birkhäuser) |
出版年 | 2010 |
大きさ | VI, 140 p : online resource |
著者標目 | *Østvær, Paul Arne author SpringerLink (Online service) |
件 名 | LCSH:Algebraic topology LCSH:Functional analysis FREE:Algebraic Topology FREE:Functional Analysis |
一般注記 | 1 Introduction -- 2 Preliminaries -- 2.1 C*-spaces -- 2.2 G – C*-spaces -- 2.3 Model categories -- 3 Unstable C*-homotopy theory -- 3.1 Pointwise model structures -- 3.2 Exact model structures -- 3.3 Matrix invariant model structures -- 3.4 Homotopy invariant model structures -- 3.5 Pointed model structures -- 3.6 Base change -- 4 Stable C*-homotopy theory -- 4.1 C*-spectra -- 4.2 Bispectra -- 4.3 Triangulated structure -- 4.4 Brown representability -- 4.5 C*-symmetric spectra -- 4.6 C*-functors -- 5 Invariants -- 5.1 Cohomology and homology theories -- 5.2 KK-theory and the Eilenberg-MacLane spectrum -- 5.3 HL-theory and the Eilenberg-MacLane -- 5.4 The Chern-Connes-Karoubi character -- 5.5 K-theory of C*-algebras -- 5.6 Zeta functions -- 6 The slice filtration -- References -- Index Homotopy theory and C*-algebras are central topics in contemporary mathematics. This book introduces a modern homotopy theory for C*-algebras. One basic idea of the setup is to merge C*-algebras and spaces studied in algebraic topology into one category comprising C*-spaces. These objects are suitable fodder for standard homotopy theoretic moves, leading to unstable and stable model structures. With the foundations in place one is led to natural definitions of invariants for C*-spaces such as homology and cohomology theories, K-theory and zeta-functions. The text is largely self-contained. It serves a wide audience of graduate students and researchers interested in C*-algebras, homotopy theory and applications HTTP:URL=https://doi.org/10.1007/978-3-0346-0565-6 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9783034605656 |
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EB00199026 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA612-612.8 DC23:514.2 |
書誌ID | 4000119835 |
ISBN | 9783034605656 |
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