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Advances in Complex Function Theory (Lecture Notes in Mathematics) by W. E. Kirwan (Repost)
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Homotopy Theory: An Introduction to Algebraic Topology (Pure and applied mathematics, 64)
Posted on 2010-04-12
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More Homotopy theory is one of the hardcore topics in algebraic topology that usually takes a formidable amount of technical machinery in order to progress in its development. This is somewhat paradoxical considering that defining homotopy groups is very straightforward. The author has given the reader a fine introduction to homotopy theory in this book, and one that still could be read even now, in spite of the developments in homotopy theory that have taken place since the book was published (1975). The book emphasizes how homotopy theory fits in with the rest of algebraic topology, and so less emphasis is placed on the actual calculation of homotopy groups, although there is enough of the latter to satisfy the reader's curiosity in this regard. In the book the author states that "the deeper one gets into mathematics, the closer one sees the connections". This is readily apparent in his coverage, as he gives a good general view of how algebra and topology are intertwined in the study of homotopy theory.
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