Lectures on algebraic topology : reprint of the 1972 edition
Lectures on algebraic topology : reprint of the 1972 edition
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DOI：
10.1007/978-3-662-00756-3
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发表时间：
1972
期刊：
影响因子：
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通讯作者：
A. Dold
中科院分区：
文献类型：
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作者：
A. Dold
这基本上是一本书奇异的同源性和上同调，特别强调产品和流形。它不处理同伦理论除了一些基本概念，一些例子，和一些应用（余）同调同伦。它也没有处理一般（-ised）同源性，但许多配方和论点的奇异同源性是如此选择，他们也适用于一般的同源性。由于这些缺席，我也省略了谱序列，其主要应用在拓扑同伦和一般（上）同调理论。切赫上同调是在一个简单的特设方式处理局部紧子集的流形;一个简短的系统治疗任意空间，强调普适性的切赫程序，载于附录。这本书成长了一个为期一年的课程代数拓扑，它可以作为一个文本这样一个课程。对于较短的基础课程，例如半年，可以使用第二、第三、第四章（第1-4节）、第五章（第1-5、7、8节）、第六章（第3、7、9、11、12节）。作为先决条件，学生应该知道一般拓扑学的基本部分，阿贝尔群理论，和语言的范畴，虽然我们的第一章提供了一点帮助，与后两个。出于教学的原因，我只在第六章之前处理了积分同调;如果读者或教师喜欢从一开始就有一般系数，他只需要做一些小的修改。
This is essentially a book on singular homology and cohomology with special emphasis on products and manifolds. It does not treat homotopy theory except for some basic notions, some examples, and some applica tions of (co-) homology to homotopy. Nor does it deal with general (-ised) homology, but many formulations and arguments on singular homology are so chosen that they also apply to general homology. Because of these absences I have also omitted spectral sequences, their main applications in topology being to homotopy and general (co-) homology theory. Cech cohomology is treated in a simple ad hoc fashion for locally compact subsets of manifolds; a short systematic treatment for arbitrary spaces, emphasizing the universal property of the Cech-procedure, is contained in an appendix. The book grew out of a one-year's course on algebraic topology, and it can serve as a text for such a course. For a shorter basic course, say of half a year, one might use chapters II, III, IV (§§ 1-4), V (§§ 1-5, 7, 8), VI (§§ 3, 7, 9, 11, 12). As prerequisites the student should know the elementary parts of general topology, abelian group theory, and the language of categories-although our chapter I provides a little help with the latter two. For pedagogical reasons, I have treated integral homology only up to chapter VI; if a reader or teacher prefers to have general coefficients from the beginning he needs to make only minor adaptions.