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  • © 1989

Grassmannians and Gauss Maps in Piecewise-Linear Topology

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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
  2. Introduction

    • Norman Levitt
    Pages 1-10
  3. Local formulae for characteristic classes

    • Norman Levitt
    Pages 11-42
  4. Some variations of the G n,k construction

    • Norman Levitt
    Pages 60-69
  5. Some applications to smoothing theory

    • Norman Levitt
    Pages 161-180
  6. 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.

Keywords

  • 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

  • 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, Differential Geometry

Buying options

eBook USD 34.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 46.00
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions