Mendeley出力
＜図書＞
Basic noncommutative geometry
| 責任表示 | Massoud Khakhali |
|---|---|
| シリーズ | EMS series of lectures in mathematics |
| データ種別 | 図書 |
| 出版情報 | Zürich : European Mathematical Society , c2009 |
| 本文言語 | 英語 |
| 大きさ | xvi, 223 p. ; 24 cm |
| 概要 | "Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for s...lf-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.続きを見る |
| 目次 | Examples of algebra-geometry correspondences Noncommutative quotients Cyclic cohomology Connes-Chern character Appendices: Gelfand-Naimark theorems Compact operators, Fredholm operators, and abstract index theory Projective modules Equivalence of categories. |
所蔵情報
| 状態 | 巻次 | 所蔵場所 | 請求記号 | 刷年 | 文庫名称 | 資料番号 | コメント | 予約・取寄 | 複写申込 | 自動書庫 |
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理系図3F 数理独自 | KHAL/20/1 | 2009 |
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023212009007220 |
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書誌詳細
| 一般注記 | Includes bibliographical references (p. [209]-218) |
|---|---|
| 著者標目 | *Khalkhali, Masoud, 1956- |
| 件 名 | LCSH:Noncommutative differential geometry |
| 分 類 | LCC:QC20.7.D52 |
| 書誌ID | 1001413885 |
| ISBN | 9783037190616 |
| NCID | BB00816507 |
| 巻冊次 | ISBN:9783037190616 |
| 登録日 | 2010.02.16 |
| 更新日 | 2010.02.16 |