Lecture Notes on Elementary Topology and Geometry

  • I. M. Singer
  • J. A. Thorpe

Part of the Undergraduate Texts in Mathematics book series (UTM)

Table of contents

  1. Front Matter
    Pages i-viii
  2. I. M. Singer, J. A. Thorpe
    Pages 1-25
  3. I. M. Singer, J. A. Thorpe
    Pages 26-48
  4. I. M. Singer, J. A. Thorpe
    Pages 49-77
  5. I. M. Singer, J. A. Thorpe
    Pages 78-108
  6. I. M. Singer, J. A. Thorpe
    Pages 109-152
  7. I. M. Singer, J. A. Thorpe
    Pages 153-174
  8. I. M. Singer, J. A. Thorpe
    Pages 175-215
  9. I. M. Singer, J. A. Thorpe
    Pages 216-229
  10. Back Matter
    Pages 230-232

About this book

Introduction

At the present time, the average undergraduate mathematics major finds mathematics heavily compartmentalized. After the calculus, he takes a course in analysis and a course in algebra. Depending upon his interests (or those of his department), he takes courses in special topics. Ifhe is exposed to topology, it is usually straightforward point set topology; if he is exposed to geom­ etry, it is usually classical differential geometry. The exciting revelations that there is some unity in mathematics, that fields overlap, that techniques of one field have applications in another, are denied the undergraduate. He must wait until he is well into graduate work to see interconnections, presumably because earlier he doesn't know enough. These notes are an attempt to break up this compartmentalization, at least in topology-geometry. What the student has learned in algebra and advanced calculus are used to prove some fairly deep results relating geometry, topol­ ogy, and group theory. (De Rham's theorem, the Gauss-Bonnet theorem for surfaces, the functorial relation of fundamental group to covering space, and surfaces of constant curvature as homogeneous spaces are the most note­ worthy examples.) In the first two chapters the bare essentials of elementary point set topology are set forth with some hint ofthe subject's application to functional analysis.

Keywords

Algebraische Topologie CON_D030 Differentialgeometrie Geometry Topologie Topology

Authors and affiliations

  • I. M. Singer
    • 1
  • J. A. Thorpe
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeUSA
  2. 2.Department of MathematicsSUNY at Stony BrookStony BrookUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4615-7347-0
  • Copyright Information Springer-Verlag New York 1967
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4615-7349-4
  • Online ISBN 978-1-4615-7347-0
  • Series Print ISSN 0172-6056
  • Series Online ISSN 1867-5514
  • About this book