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Grassmannians and Gauss Maps in Piecewise-Linear Topology

  • Book
  • © 1989

Overview

Authors:
  1. Norman Levitt
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1366)

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Table of contents (11 chapters)

  1. Front Matter

    Pages I-V
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  2. Introduction

    • Norman Levitt
    Pages 1-10

  3. Local formulae for characteristic classes

    • Norman Levitt
    Pages 11-42

  4. Formal links and the PL grassmannian G n,k

    • Norman Levitt
    Pages 43-59

  5. Some variations of the G n,k construction

    • Norman Levitt
    Pages 60-69

  6. The immersion theorem for subcomplexes of G n,k

    • Norman Levitt
    Pages 70-86

  7. Immersions equivariant with respect to orthogonal actions on Rn+k

    • Norman Levitt
    Pages 87-100

  8. Immersions into triangulated manifolds (with R. Mladineo)

    • Norman Levitt
    Pages 101-115

  9. The grassmannian for piecewise smooth immersions

    • Norman Levitt
    Pages 116-160

  10. Some applications to smoothing theory

    • Norman Levitt
    Pages 161-180

  11. Equivariant piecewise differentiable immersions

    • Norman Levitt
    Pages 181-187

  12. Piecewise differentiable immersions into riemannian manifolds

    • Norman Levitt
    Pages 188-197

  13. Back Matter

    Pages 198-203
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Keywords

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.

Bibliographic Information

  • Book Title: Grassmannians and Gauss Maps in Piecewise-Linear Topology

  • Authors: Norman Levitt

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0084994

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-50756-7Published: 22 February 1989

  • eBook ISBN: 978-3-540-46078-7Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: V, 203

  • Topics: Manifolds and Cell Complexes (incl. Diff.Topology), Differential Geometry

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