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Introduction to Differential Manifolds

  • Serge Lang

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Pages 20-36
  3. Pages 37-59
  4. Pages 143-157
  5. Pages 158-179
  6. Pages 200-213
  7. Back Matter
    Pages 243-250

About this book

Introduction

"This book contains essential material that every graduate student must know. Written with Serge Lang's inimitable wit and clarity, the volume introduces the reader to manifolds, differential forms, Darboux's theorem, Frobenius, and all the central features of the foundations of differential geometry. Lang lays the basis for further study in geometric analysis, and provides a solid resource in the techniques of differential topology. The book will have a key position on my shelf.
Steven Krantz, Washington University in St. Louis

"This is an elementary, finite dimensional version of the author's classic monograph, Introduction to Differentiable Manifolds (1962), which served as the standard reference for infinite dimensional manifolds. It provides a firm foundation for a beginner's entry into geometry, topology, and global analysis. The exposition is unencumbered by unnecessary formalism, notational or otherwise, which is a pitfall few writers of introductory texts of the subject manage to avoid. The author's hallmark characteristics of directness, conciseness, and structural clarity are everywhere in evidence. A nice touch is the inclusion of more advanced topics at the end of the book, including the computation of the top cohomology group of a manifold, a generalized divergence theorem of Gauss, and an elementary residue theorem of several complex variables. If getting to the main point of an argument or having the key ideas of a subject laid bare is important to you, then you would find the reading of this book a satisfying experience."
Hung-Hsi Wu, University of California, Berkeley

Keywords

Area Volume differential geometry differential topology manifold topology

Authors and affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

Bibliographic information