By John M. Lee

ISBN-10: 1441999825

ISBN-13: 9781441999825

This ebook is an introductory graduate-level textbook at the concept of soft manifolds. Its objective is to familiarize scholars with the instruments they'll desire with the intention to use manifolds in mathematical or medical research—smooth constructions, tangent vectors and covectors, vector bundles, immersed and embedded submanifolds, tensors, differential varieties, de Rham cohomology, vector fields, flows, foliations, Lie derivatives, Lie teams, Lie algebras, and extra. The strategy is as concrete as attainable, with photographs and intuitive discussions of the way one may still imagine geometrically concerning the summary strategies, whereas making complete use of the strong instruments that glossy arithmetic has to offer.

This moment variation has been commonly revised and clarified, and the themes were considerably rearranged. The e-book now introduces the 2 most crucial analytic instruments, the rank theorem and the basic theorem on flows, a lot previous which will be used through the ebook. a number of new subject matters were additional, significantly Sard’s theorem and transversality, an evidence that infinitesimal Lie workforce activities generate international crew activities, a extra thorough research of first-order partial differential equations, a short remedy of measure idea for gentle maps among compact manifolds, and an advent to touch structures.

Prerequisites contain a superb acquaintance with normal topology, the elemental staff, and masking areas, in addition to uncomplicated undergraduate linear algebra and genuine research.