Homotopical Topology (Graduate Texts in Mathematics Book 273) 2nd Edition by Anatoly Fomenko (PDF)

Description

This textbook on algebraic topology updates a popular textbook from the golden era of the Moscow school of I. M. Gelfand. The first English translation, done many decades ago, remains very much in demand, although it has been long out-of-print and is difficult to obtain. Therefore, this updated English edition will be much welcomed by the mathematical community. Distinctive features of this book include: a concise but fully rigorous presentation, supplemented by a plethora of illustrations of a high technical and artistic caliber; a huge number of nontrivial examples and computations done in detail; a deeper and broader treatment of topics in comparison to most beginning books on algebraic topology; an extensive, and very concrete, treatment of the machinery of spectral sequences. The second edition contains an entirely new chapter on K-theory and the Riemann-Roch theorem (after Hirzebruch and Grothendieck).

User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐This book is different from most of the other standard textbooks in that it does not follow the usual “definition-lemma-theorem-application-more definition” paradigm. The authors try to give intuition, and on many a occasion leaves the technicalities to be supplied by the reader. Covers a wide range of topic starting from standard homotopy theory, to homology and cohomology, to even extra-ordinary cohomology theories (k-theory), and yet sticks to mostly classical (geometric) spaces for examples. Due to this emphasis, while reading this book, the reader is not going to lose himself in (for example) simplicial mambo-jumbo of Jardine, or winding number excessive of Fulton. Also, the content has been presented wisely and meticulously.Highly recommended.

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