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-Čech 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.
Additional ISBNs
9781439848142, 1439848149
An Illustrated Introduction to Topology and Homotopy Ebook
By: Sasho Kalajdzievski
Publisher:
Chapman and Hall/CRC
Print ISBN: 9781439848159, 1439848157
eText ISBN: 9781482220810, 1482220814
Edition: 1st
Copyright year: 2014
Format: PDF
Available from $ 23.18 USD
SKU: 9781482220810R90
? Downloaded copy on your device does not expire..
?
