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Introduction to Smooth Manifolds (Paperback, 2nd ed. 2012)
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Introduction to Smooth Manifolds (Paperback, 2nd ed. 2012)
Series: Graduate Texts in Mathematics, 218
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This book is an introductory graduate-level textbook on the theory
of smooth manifolds. Its goal is to familiarize students with the
tools they will need in order to use manifolds in mathematical or
scientific research--- smooth structures, tangent vectors and
covectors, vector bundles, immersed and embedded submanifolds,
tensors, differential forms, de Rham cohomology, vector fields,
flows, foliations, Lie derivatives, Lie groups, Lie algebras, and
more. The approach is as concrete as possible, with pictures and
intuitive discussions of how one should think geometrically about
the abstract concepts, while making full use of the powerful tools
that modern mathematics has to offer. This second edition has been
extensively revised and clarified, and the topics have been
substantially rearranged. The book now introduces the two most
important analytic tools, the rank theorem and the fundamental
theorem on flows, much earlier so that they can be used throughout
the book. A few new topics have been added, notably Sard's theorem
and transversality, a proof that infinitesimal Lie group actions
generate global group actions, a more thorough study of first-order
partial differential equations, a brief treatment of degree theory
for smooth maps between compact manifolds, and an introduction to
contact structures. Prerequisites include a solid acquaintance with
general topology, the fundamental group, and covering spaces, as
well as basic undergraduate linear algebra and real analysis.
General
Imprint: |
Springer-Verlag New York
|
Country of origin: |
United States |
Series: |
Graduate Texts in Mathematics, 218 |
Release date: |
September 2014 |
First published: |
2012 |
Authors: |
John Lee
|
Dimensions: |
235 x 155 x 43mm (L x W x T) |
Format: |
Paperback
|
Pages: |
708 |
Edition: |
2nd ed. 2012 |
ISBN-13: |
978-1-4899-9475-2 |
Categories: |
Books >
Science & Mathematics >
Mathematics >
Geometry >
Differential & Riemannian geometry
|
LSN: |
1-4899-9475-0 |
Barcode: |
9781489994752 |
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