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# Notes On The Course Algebraic Topology by Boris Botvinnik

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Notes On The Course Algebraic Topology written by Boris Botvinnik .
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.

Book Detail :-
Title: Notes On The Course Algebraic Topology
Edition:
Author(s): Boris Botvinnik
Publisher:
Series:
Year:
Pages: 181
Type: PDF
Language: English
ISBN:
Country:
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Book Contents :-
Notes On The Course Algebraic Topology written by Boris Botvinnik cover the following topics.
1. Important examples of topological spaces
2. Constructions
3. Homotopy and homotopy equivalence
4. CW -complexes
5. CW -complexes and homotopy
6. Fundamental group
7. Covering spaces
8. Higher homotopy groups
9. Fiber bundles
10. Suspension Theorem and Whitehead product
11. Homotopy groups of CW -complexes
12. Homology groups: basic constructions
13. Homology groups of CW -complexes
14. Homology and homotopy groups
15. Homology with coefficients and cohomology groups
16. Some applications
17. Cup product in cohomology.
18. Cap product and the Poincare duality.
19. Hopf Invariant
20. Elementary obstruction theory
21. Cohomology of some Lie groups and Stiefel manifolds

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