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Basic Algebraic Topology and its Applications (Paperback, Softcover reprint of the original 1st ed. 2016)
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Basic Algebraic Topology and its Applications (Paperback, Softcover reprint of the original 1st ed. 2016)
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This book provides an accessible introduction to algebraic
topology, a field 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 offers
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.
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