© 1989

Grassmannians and Gauss Maps in Piecewise-linear Topology

  • Authors

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


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.


Immersion curvature differential geometry differential topology manifold topology

Bibliographic information

  • Book Title Grassmannians and Gauss Maps in Piecewise-linear Topology
  • Authors Norman Levitt
  • Series Title Lecture Notes in Mathematics
  • Series Abbreviated Title Lecture Notes in Mathematics
  • DOI
  • Copyright Information Springer-Verlag Berlin Heidelberg 1989
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Softcover ISBN 978-3-540-50756-7
  • eBook ISBN 978-3-540-46078-7
  • Series ISSN 0075-8434
  • Series E-ISSN 1617-9692
  • Edition Number 1
  • Number of Pages V, 203
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Manifolds and Cell Complexes (incl. Diff.Topology)
    Differential Geometry
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