Logo - springer
Slogan - springer

Mathematics - Geometry & Topology | Introduction to Smooth Manifolds

Introduction to Smooth Manifolds

Series: Graduate Texts in Mathematics, Vol. 218

Lee, John

2nd ed. 2013, XVI, 708 p.

Available Formats:
eBook
Information

Springer eBooks may be purchased by end-customers only and are sold without copy protection (DRM free). Instead, all eBooks include personalized watermarks. This means you can read the Springer eBooks across numerous devices such as Laptops, eReaders, and tablets.

You can pay for Springer eBooks with Visa, Mastercard, American Express or Paypal.

After the purchase you can directly download the eBook file or read it online in our Springer eBook Reader. Furthermore your eBook will be stored in your MySpringer account. So you can always re-download your eBooks.

 
$69.99

(net) price for USA

ISBN 978-1-4419-9982-5

digitally watermarked, no DRM

Included Format: PDF

download immediately after purchase


learn more about Springer eBooks

add to marked items

Hardcover
Information

Hardcover version

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$99.00

(net) price for USA

ISBN 978-1-4419-9981-8

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

Softcover
Information

Softcover (also known as softback) version.

You can pay for Springer Books with Visa, Mastercard, American Express or Paypal.

Standard shipping is free of charge for individual customers.

 
$99.00

(net) price for USA

ISBN 978-1-4899-9475-2

free shipping for individuals worldwide

usually dispatched within 3 to 5 business days


add to marked items

  • New edition extensively revised and clarified, and topics have been substantially rearranged
  • Introduces the two most important analytic tools, the rank theorem and the fundamental theorem on flows, much earlier in the text
  • Added topics include  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

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.

Content Level » Graduate

Keywords » Frobenius theorem - Lie group - Sard’s theorem - Smooth structures - Stokes's theorem - Tangent vectors and covectors - Whitney approximation theorem - Whitney embedding theorem - de Rham cohomology - differential forms - first-order partial differential equations - foliations - immersed and embedded submanifolds - smooth manifolds - tensors - vector bundles - vector fields and flows

Related subjects » Geometry & Topology

Table of contents / Preface / Sample pages 

Popular Content within this publication 

 

Articles

Read this Book on Springerlink

Services for this book

New Book Alert

Get alerted on new Springer publications in the subject area of Differential Geometry.