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 selfcontained 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 StoneCech 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 Seifertvan Kampen theorem, knots, and lowdimensional manifolds. The last three chapters discuss the theory of covering spaces, the BorsukUlam 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.
About Sasho Kalajdzievski
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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 
Rating  : 
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