Introduction to Smooth Manifolds John Lee’s an English-language textbook that provides a clear introduction to the mathematical theory of smooth manifolds. The book is aimed at students and researchers who want to delve into the fundamental concepts and techniques of differential geometry.
The contents cover topics such as smooth structures, tangent vectors, vector bundles, immersions, tensors, differential forms, de Rham cohomology, flows, foliations, Lie groups, and Lie algebras. The second edition has been thoroughly revised; topics have been rearranged and expanded with, among other things, Sard’s theorem, transversality, and contact structures. Essential analytical tools such as the rank theorem and the fundamental theorem about flows are introduced early, strengthening the book’s applicability throughout.
Prerequisite knowledge of general topology, fundamental groups, basic linear algebra, and real analysis is required. The approach is concrete, with illustrations and intuitive explanations, which makes this book an important introduction to smooth manifolds within the graduate texts in mathematics.
Series: Graduate Texts in Mathematics