Grassmannians and Gauss Maps in Piecewise-linear Topology

  • Authors
  • NormanĀ Levitt

Part of the Lecture Notes in Mathematics book series (LNM, volume 1366)

Table of contents

  1. Front Matter
    Pages I-V
  2. Norman Levitt
    Pages 1-10
  3. Norman Levitt
    Pages 11-42
  4. Norman Levitt
    Pages 43-59
  5. Norman Levitt
    Pages 60-69
  6. Norman Levitt
    Pages 161-180
  7. Back Matter
    Pages 198-203

About this book

Introduction

The book explores the possibility of extending the notions of "Grassmannian" and "Gauss map" to the PL category. They are distinguished from "classifying space" and "classifying map" which are essentially homotopy-theoretic notions. The analogs of Grassmannian and Gauss map defined incorporate geometric and combinatorial information. Principal applications involve characteristic class theory, smoothing theory, and the existence of immersion satifying certain geometric criteria, e.g. curvature conditions. The book assumes knowledge of basic differential topology and bundle theory, including Hirsch-Gromov-Phillips theory, as well as the analogous theories for the PL category. The work should be of interest to mathematicians concerned with geometric topology, PL and PD aspects of differential geometry and the geometry of polyhedra.

Keywords

Immersion curvature differential geometry differential topology manifold topology

Bibliographic information

  • DOI https://doi.org/10.1007/BFb0084994
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-50756-7
  • Online ISBN 978-3-540-46078-7
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book