Provides a comprehensive treatment of basic topology and homotopy that uses a combination of rigorous proofs and extensive visualization Gives full details of most proofs Contains nearly 600 figures that help clarify difficult concepts Presents historical notes that outline the growth of the subject Includes about 750 exercises, many of which are relatively new Offers figures for each chapter on the author’s website Forthcoming solutions manual available upon qualifying course adoption Summary 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.
- ISBN: 9781439848159
- Editorial: CHAPMAN & HALL LTD.
- Encuadernacion: Tela
- Páginas: 485
- Fecha Publicación: 24/05/2015
- Nº Volúmenes: 1
- Idioma: