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About this book :-
A Concise Course in Algebraic Topology written by
J. P. May .
This book provides an accessible introduction to algebraic topology, a ?eld at the intersection of topology, geometry and algebra, together with its applications. Moreover, it covers several related topics that are in fact important in the overall scheme of algebraic topology. Comprising eighteen chapters and two appendices, the book integrates various concepts of algebraic topology, supported by examples, exercises, applications and historical notes. Primarily intended as a textbook, the book o?ers a valuable resource for undergraduate, postgraduate and advanced mathematics students alike. Focusing more on the geometric than on algebraic aspects of the subject, as well as its natural development, the book conveys the basic language of modern algebraic topology by exploring homotopy, homology and cohomology theories, and examines a variety of spaces: spheres, projective spaces, classical groups and their quotient spaces, function spaces, polyhedra, topological groups, Lie groups and cell complexes, etc. The book studies a variety of maps, which are continuous functions between spaces. It also reveals the importance of algebraic topology in contemporary mathematics, theoretical physics, computer science, chemistry, economics, and the biological and medical sciences, and encourages students to engage in further study. Algebraic topology is one of the most important creations in mathematics which uses algebraic tools to study topological spaces. The basic goal is to find algebraic invariants that classify topological spaces up to homeomorphism (though usually classify up to homotopy equivalence). The most important of these invariants are homotopy groups, homology groups, and cohomology groups (rings). The main purpose of this book is to give an accessible presentation to the readers of the basic materials of algebraic topology through a study of homotopy, homology, and cohomology theories. Moreover, it covers a lot of topics for advanced students who are interested in some applications of the materials they have been taught. Several basic concepts of algebraic topology, and many of their successful applications in other areas of mathematics and also beyond mathematics with surprising results have been given. The essence of this method is a transformation of the geometric problem to an algebraic one which offers a better chance for solution by using standard algebraic methods.
(Mahima Ranjan Adhikari)
Book Detail :-
Title: A Concise Course in Algebraic Topology
Edition:
Author(s): J. P. May
Publisher:
Series:
Year: 1999
Pages: 251
Type: PDF
Language: English
ISBN: 0226511839, 978-0226511832
Country: US
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About Author :-
J. P. May , is professor of mathematics at the University of Chicago; he is the author or coauthor of many papers and books, including Simplicial Objects in Algebraic Topology and A Concise Course in Algebraic Topology, both in the Chicago Lectures in Mathematics series.
All Famous Books of this Author :-
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The author • Download PDF Basic Algebraic Topology and its Applications by Mahima Adhikari
The author • Download PDF A Concise Course in Algebraic Topology by J. P. May
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Book Contents :-
A Concise Course in Algebraic Topology written by
J. P. May
cover the following topics.
1. The fundamental group and some of its applications
2. Categorical language and the van Kampen theorem
3. Covering spaces
4. Graphs
5. Compactly generated spaces
6. Cofibrations
7. Fibrations
8. Based cofiber and fiber sequences
9. Higher homotopy groups
10. CW complexes
11. The homotopy excision and suspension theorems
12. A little homological algebra
13. Axiomatic and cellular homology theory
14. Derivations of properties from the axioms
15. The Hurewicz and uniqueness theorems
16. Singular homology theory
17. Some more homological algebra
18. Axiomatic and cellular cohomology theory
19. Derivations of properties from the axioms
20. The Poincar´e duality theorem
21. The index of manifolds; manifolds with boundary
22. Homology, cohomology, and K(p, n)s
23. Characteristic classes of vector bundles
24. An introduction to K-theory
25. An introduction to cobordism
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