An Illustrated Introduction to Topology and Homotopy PDF ePub eBook

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An Illustrated Introduction to Topology and Homotopy free pdf An Illustrated Introduction to Topology and Homotopy explores the beauty of topology and homotopy theory in a direct and engaging manner while illustrating the power of the theory through many, often surprising, applications. This self-contained book takes a visual and rigorous approach that incorporates both extensive illustrations and full proofs. The first part of the text covers basic topology, ranging from metric spaces and the axioms of topology through subspaces, product spaces, connectedness, compactness, and separation axioms to Urysohn's lemma, Tietze's theorems, and Stone-Cech compactification. Focusing on homotopy, the second part starts with the notions of ambient isotopy, homotopy, and the fundamental group. The book then covers basic combinatorial group theory, the Seifert-van Kampen theorem, knots, and low-dimensional manifolds. The last three chapters discuss the theory of covering spaces, the Borsuk-Ulam theorem, and applications in group theory, including various subgroup theorems. Requiring only some familiarity with group theory, the text includes a large number of figures as well as various examples that show how the theory can be applied. Each section starts with brief historical notes that trace the growth of the subject and ends with a set of exercises.

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Details Book

Author : Sasho Kalajdzievski
Publisher : Chapman
Data Published : 23 March 2015
ISBN : 1439848157
EAN : 9781439848159
Format Book : PDF, Epub, DOCx, TXT
Number of Pages : 485 pages
Age + : 15 years
Language : English
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