Fundamentals of Algebraic Topology

Steven H. Weintraub is Professor of Mathematics at Lehigh University. He is the author of Galois Theory and Algebra: An Approach via Module Theory (with W. A. Adkins).

"Weinberg front-loads the Eilenberg-Steenrod axioms, thus rendering singular homology, where most authors start, merely an important example that emerges well on in the text. Certain readers either primarily interested in making calculations or in 'extraordinary' theories such as K-theories or (co)bordism will appreciate this emphasis. Summing Up: Recommended. Upper-division undergraduates and above." (D. V. Feldman, Choice, Vol. 52 (10), June, 2015) "The fundamental group, covering spaces, a heavy dose of homology theory, applications to manifolds, and the higher homotopy groups is what the book is all about. ... The exposition is exquisite, making reading the book very enjoyable. The book certainly has its place among the existing literature, as it offers something different from its peers. ... All in all, what the book does it does very well, and it achieves a lot. ... Certainly a recommended read." (Ittay Weiss, MAA Reviews, March, 2015) "This new booklet by the renowned textbook author Steven H. Weintraub is to serve as a quick guide to the fundamental concepts and results of classical algebraic topology. ... the present book is certainly a highly useful and valuable companion for a first-year graduate course in algebraic topology, as well for ambitious students as for instructors." (Werner Kleinert, zbMATH, Vol. 1305, 2015)

• Preface.-​ ​1. The Basics.- 2. The Fundamental Group.- 3. Generalized Homology Theory.- 4. Ordinary Homology Theory.- 5. Singular Homology Theory.- 6. Manifolds.- 7. Homotopy Theory.- 8. Homotopy Theory.- A. Elementary Homological Algebra.- B. Bilinear Forms.- C. Categories and Functors.- Bibliography.- Index.