Simplicial Homotopy Theory
Simplicial Homotopy Theory
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DOI：
10.1007/978-3-0346-0189-4
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
P. Goerss;J. Jardine
中科院分区：
文献类型：
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作者：
P. Goerss;J. Jardine
自现代代数拓扑学诞生以来，单纯形方法在计算和基本理论中得到了系统而有效的应用。随着Quillen闭模型范畴概念的发展，特别是单纯模型范畴的发展，这种方法集合已经成为描述非交换同调代数和解决包括代数K-理论在内的各种领域中同伦理论问题的主要方法。这本书对这些思想进行了现代阐释，强调了模型范畴的理论技术。这里讨论的是单纯集的同伦理论，以及其他基本主题，如单纯群、波斯尼科夫塔和双单纯集。更高级的材料包括同伦极限和同伦极限、关于映射和关于同调理论的局部化、余单纯空间和同伦连贯性。贯穿始终的是许多专家熟知的结果和想法，但在文献中没有收集到。旨在为二年级研究生和以后，这本书介绍了许多现代同伦理论的基本工具。我们并不假定你有丰富的拓扑学背景。评论：“……一本填补了文学上的一个明显空白的书，作者们在这本书上做得很好。在过去的28年里，没有发表过关于这个主题的专著或说明性论文。每一章之前都有一个简短的摘要，这对读者是有用的。这本书应该被证明是对广大读者的启发，包括潜在的学生和研究人员，他们想要应用简单的技术，无论出于什么原因。他们成功了。这本书从现代的角度很好地描述了单纯同伦理论[…]这本书写得很好。这本书可以强烈推荐给任何想要学习和应用简单技术和/或(单纯)封闭模型范畴理论的人。
Since the beginning of the modern era of algebraic topology, simplicial methods have been used systematically and effectively for both computation and basic theory. With the development of Quillen's concept of a closed model category and, in particular, a simplicial model category, this collection of methods has become the primary way to describe non-abelian homological algebra and to address homotopy-theoretical issues in a variety of fields, including algebraic K-theory. This book supplies a modern exposition of these ideas, emphasizing model category theoretical techniques. Discussed here are the homotopy theory of simplicial sets, and other basic topics such as simplicial groups, Postnikov towers, and bisimplicial sets. The more advanced material includes homotopy limits and colimits, localization with respect to a map and with respect to a homology theory, cosimplicial spaces, and homotopy coherence. Interspersed throughout are many results and ideas well-known to experts, but uncollected in the literature. Intended for second-year graduate students and beyond, this book introduces many of the basic tools of modern homotopy theory. An extensive background in topology is not assumed. Reviews:"... a book filling an obvious gap in the literature and the authors have done an excellent job on it. No monograph or expository paper has been published on this topic in the last twenty-eight years."-Analele Universitatii din Timisoara"... is clearly presented and a brief summary preceding every chapter is useful to the reader. The book should prove enlightening to a broad range of readers including prospective students and researchers who want to apply simplicial techniques for whatever reason."-Zentralblatt MATH"... they succeed. The book is an excellent account of simplicial homotopy theory from a modern point of view [...] The book is well written.[...] The book can be highly recommended to anybody who wants to learn and to apply simplicial techniques and/or the theory of (simplicial) closed model categories."-Mathematical Reviews