Comments:

Revised, 243 pages, year: 1999, The University of Chicago Press: Chicago and London

Abstract:

An intermediate to advanced, mathematics graduate book covering a wide range of topics, stressing category theory and homological algebra-- which is organized in 25 chapters that include but are not limited to: homotopy invariance, cohomology axioms, derived cohomology theorems, Postnikov systems, approximation theorem, colimits, pushouts, localization, axiomatic and cellular cohomology theory, homology theory, duality, cobordism, homological algebra and category theory, K-theory, Hopf algebras, derivations from axioms, groupoids, fundamental groupoid, categories, graphs, covering spaces, Eilenberg-MacLane spaces, CW complexes, compactly generated spaces, higher homotopy groups. Has a brief Index and also suggested references for further reading in Algebraic Topology, and all the topics listed here that are covered in the book at an accessible level. Another Synposis introducing this book is quoted here verbatim: ``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 detailed 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 over the past several decades, 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 that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.'' A review of this and other books by the same author can be downloaded as a PDF at http://math.vassar.edu/faculty/McCleary/May.review.pdf

Rights:

currently open, revised version Copyright@1999, The University of Chicago, http://www.math.uchicago.edu/~may/CONCISE/ConciseRevised.pdf

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