A course on manifolds differs from most other introductory mathematics graduate courses in that the subject matter is often completely unfamiliar. In his beautifully conceived Introduction the author motivates what is to follow in the book by explaining the roles manifolds play in topology, geometry, complex analysis, algebra, classical mechanics, and general relativity. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces. The pace is leisurely; the book is aimed at beginning graduate students.

Klappentext

Manifolds play an important role in topology, geometry, complex analysis, algebra, and classical mechanics. Learning manifolds differs from most other introductory mathematics in that the subject matter is often completely unfamiliar. This introduction guides readers by explaining the roles manifolds play in diverse branches of mathematics and physics. The book begins with the basics of general topology and gently moves to manifolds, the fundamental group, and covering spaces.

Inhalt

Topological Spaces.- New Spaces from Old.- Connectedness and Compactness.- Simplicial Complexes.- Curves and Surfaces.- Homotopy and the Fundamental Group.- Circles and Spheres.- Some Group Theory.- The Seifert-Van Kampen Theorem.- Covering Spaces.- Classification of Coverings.- Homology.