Introduction to Smooth Manifolds John Lee is an English-language textbook aimed at higher education and research. It thoroughly covers the theory of smooth manifolds and equips students with the tools to master these complex topics.
This textbook introduces the key concepts such as smooth structures, tangent spaces, vector bundles, immersions and embeddings, tensors, differential forms, de Rham cohomology, vector fields, Lie groups, and Lie algebras. The second edition has been revised and reorganized with an earlier introduction of analytical techniques such as the rank theorem and the theorem on flows.
New topics have been added, including Sard's theorem, transversality, the relationship between infinitesimal and global Lie group actions, first-order partial differential equations, degree theory, and contact structures. This book connects in content with topology, differential geometry, and Riemannian geometry.
Essential for students seeking a thorough introduction to smooth manifolds and wanting to work with the tools needed for research in mathematics and related sciences.
Series: Graduate Texts in Mathematics