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Rational Homotopy Type

A Constructive Study via the Theory of the I*-measure

  • Book
  • © 1987

Overview

Authors:
  1. Wu Wen-tsün
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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1264)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-VIII
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  2. Fundamental concepts. Measure and calculability

    • Wu Wen-tsün
    Pages 1-19

  3. Dga and minimal model

    • Wu Wen-tsün
    Pages 20-57

  4. The de rham-sullivan theorem and I*-measure

    • Wu Wen-tsün
    Pages 58-92

  5. I*-measure and homotopy

    • Wu Wen-tsün
    Pages 93-115

  6. I*-measure of a homogeneous space — The cartan theorem

    • Wu Wen-tsün
    Pages 116-142

  7. Effective computation and axiomatic system of I*-measure

    • Wu Wen-tsün
    Pages 143-177

  8. I*-measures connected with fibrations

    • Wu Wen-tsün
    Pages 178-213

  9. Back Matter

    Pages 214-219
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Keywords

About this book

This comprehensive monograph provides a self-contained treatment of the theory of I*-measure, or Sullivan's rational homotopy theory, from a constructive point of view. It centers on the notion of calculability which is due to the author himself, as are the measure-theoretical and constructive points of view in rational homotopy. The I*-measure is shown to differ from other homology and homotopy measures in that it is calculable with respect to most of the important geometric constructions encountered in algebraic topology. This approach provides a new method of treatment and leads to various new results. In particular, an axiomatic system of I*-measure is formulated, quite different in spirit from the usual Eilenberg-Steenrod axiomatic system for homology, and giving at the same time an algorithmic method of computation of the I*-measure in concrete cases. The book will be of interest to researchers in rational homotopy theory and will provide them with new ideas and lines of research to develop further.

Bibliographic Information

  • Book Title: Rational Homotopy Type

  • Book Subtitle: A Constructive Study via the Theory of the I*-measure

  • Authors: Wu Wen-tsün

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0081997

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1987

  • Softcover ISBN: 978-3-540-13611-8Published: 15 July 1987

  • eBook ISBN: 978-3-540-39025-1Published: 14 November 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: X, 222

  • Topics: Algebraic Topology

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