Algebraic topology is a basic part of modern mathematics and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry and Lie groups. This book provides a treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology and the book concludes with a list of suggested readings for those interested in delving further into the field.
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如标题所言,确实简洁。讲完fundamental group,马上引入一点范畴语言。
评分据说是讲代数拓扑里面最难的一本,最难不好说,观点很高倒是真的,比较多的采用代数和范畴的语言,和Hatcher,Novikov的那样的代数拓扑完全不是一个范儿,不过毋庸置疑是本极好的拓扑讲义。
评分据说是讲代数拓扑里面最难的一本,最难不好说,观点很高倒是真的,比较多的采用代数和范畴的语言,和Hatcher,Novikov的那样的代数拓扑完全不是一个范儿,不过毋庸置疑是本极好的拓扑讲义。
评分据说是讲代数拓扑里面最难的一本,最难不好说,观点很高倒是真的,比较多的采用代数和范畴的语言,和Hatcher,Novikov的那样的代数拓扑完全不是一个范儿,不过毋庸置疑是本极好的拓扑讲义。
评分图表很多,证明比较简洁。正合序列:叶化和核的关系;庞加莱对偶是代数拓扑对于几何拓扑的一个限制条件。
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