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.
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Series
39 primary booksGraduate Texts in Mathematics is a 39-book series with 39 primary works first released in 1899 with contributions by Peter J. Hilton, Urs Stammbach, and 37 others.