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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據說是講代數拓撲裏麵最難的一本,最難不好說,觀點很高倒是真的,比較多的采用代數和範疇的語言,和Hatcher,Novikov的那樣的代數拓撲完全不是一個範兒,不過毋庸置疑是本極好的拓撲講義。
评分確實不適閤初學者,隻讀到上同調,確實簡潔,不先看hatcher的話,我很難get到他的妙處……
评分確實不適閤初學者,隻讀到上同調,確實簡潔,不先看hatcher的話,我很難get到他的妙處……
评分這本加上Bredon的那本topology and geometry足以打通拓撲學任督二脈,要是本科再學一次幾何和拓撲,我隻會讀這兩本書,最多再加一本Loring W.Tu
评分圖錶很多,證明比較簡潔。正閤序列:葉化和核的關係;龐加萊對偶是代數拓撲對於幾何拓撲的一個限製條件。
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