Combinatorial Algebraic Topology
Combinatorial Algebraic Topology
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DOI：
10.1007/978-3-540-71962-5
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发表时间：
2007-10
影响因子：
1.3
通讯作者：
D. Kozlov
中科院分区：
文献类型：
--
作者：
D. Kozlov
组合代数拓扑学是代数拓扑学和离散数学的交叉领域。这本书是第一本以书的形式全面论述这个问题的书。本书的第一部分快速介绍了代数拓扑的主要工具，包括后面部分需要的Stiefel-Whitney特征类。读者——研究生和在职数学家——可能会发现第二部分特别有用，它包含了对组合代数拓扑的主要研究技术的深入讨论。我们对标准主题的表述与现有文本有很大不同。此外，还包括了一些新的主题，如光谱序列。虽然第二部分的应用是零星的，但第三部分的重点是它们，第三部分完全致力于发展图同态的拓扑结构理论。对读者来说，主要的好处将是相当快地到达这个活跃领域的现代研究的前沿。
Combinatorial algebraic topology is a fascinating and dynamic field at the crossroads of algebraic topology and discrete mathematics. This volume is the first comprehensive treatment of the subject in book form. The first part of the book constitutes a swift walk through the main tools of algebraic topology, including Stiefel-Whitney characteristic classes, which are needed for the later parts. Readers-graduate students and working mathematicians alike-will probably find particularly useful the second part, which contains an in-depth discussion of the major research techniques of combinatorial algebraic topology. Our presentation of standard topics is quite different from that of existing texts. In addition, several new themes, such as spectral sequences, are included. Although applications are sprinkled throughout the second part, they are principal focus of the third part, which is entirely devoted to developing the topological structure theory for graph homomorphisms. The main benefit for the reader will be the prospect of fairly quickly getting to the forefront of modern research in this active field.