K理论导论读书介绍
| 类别 | 页数 | 译者 | 网友评分 | 年代 | 出版社 |
|---|---|---|---|---|---|
| 书籍 | 315页 | 2020 | 世界图书出版公司北京公司 |
| 定价 | 出版日期 | 最近访问 | 访问指数 |
|---|---|---|---|
| CNY 55.00 | 2020-02-20 … | 2021-04-19 … | 43 |
AT-theory was introduced by A. Grothendieck in his formulation of the Riemann- Roch theorem (cf. Borel and Serre [2]). For each projective algebraic variety, Grothendieck constructed a group from the category of coherent algebraic sheaves, and showed that it had many nice properties. Atiyah and Hirzebruch [3] con sidered a topological analog defined for any compact space X, a group K{X) constructed from the category of vector bundles on X. It is this ''topological J DEGREES-theory" that this book will study. Topological DEGREES-theory has become an important tool in topology. Using- theory, Adams and Atiyah were able to give a simple proof that the only spheres which can be provided with //-space structures are S DEGREES, S DEGREES and S' DEGREES. Moreover, it is possible to derive a substantial part of stable homotopy theory from A DEGREES-theory (cf. J. F. Adams [2]). Further applications to analysis and algebra are found in the work of Atiyah-Singer [2], Bass [1], Quillen [1], and others. A key factor in these applications is Bott periodicity (Bott [2]). The purpose of this book is to provide advanced students and mathematicians in other fields with the fundamental material in this subject. In addition, several applications of the type described above are included. In general we have tried to make this book self-contained, beginning with elementary concepts wherever possible; however, we assume that the reader is familiar with the basic definitions of homotopy theory: homotopy cl
作者简介Max Karoubi received his PhD in mathematics (Doctorat d'Etat) from Paris University in 1967, while working in the CNRS (Centre National de la Recherche Scientifique), under the supervision of Henri Cartan and Alexander Grothendieck. After his PhD, he took a position of "Maître de Conférences" at the University of Strasbourg until 1972. He was then nominated full Professor at t...
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