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Rational homotopy type : a constructive study via the theory of the I*-measure / Wu Wen-tsün.

By: Material type: TextTextSeries: Lecture notes in mathematics (Springer-Verlag) ; 1264.Publication details: Berlin ; New York : Springer-Verlag, ©1987.Description: 1 online resource (viii, 219 pages) : illustrationsContent type:
  • text
Media type:
  • computer
Carrier type:
  • online resource
ISBN:
  • 9783540390251
  • 3540390251
Subject(s): Additional physical formats: Print version:: Rational homotopy type.DDC classification:
  • 514.24 22
LOC classification:
  • QA3 .L28 no. 1264 QA612.7
Other classification:
  • *55-02
  • 31.65
  • 55P62
  • PC 81
Online resources:
Contents:
Fundamental Concepts -- Measure and Calculability -- DGA and Minimal Model -- The DeRham-Sullivan Theorem and I*-Measure -- I*-Measure and Homotopy -- I*-Measure of a Homogeneous Space -- The Cartan Theorem -- Effective Computation and Axiomatic System of I*-Measure -- I*-Measures Connected with Fibrations -- Bibliography -- Index.
Action note:
  • digitized 2010 HathiTrust Digital Library committed to preserve
Summary: 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.
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Includes bibliographical references (pages 214-217) and index.

Fundamental Concepts -- Measure and Calculability -- DGA and Minimal Model -- The DeRham-Sullivan Theorem and I*-Measure -- I*-Measure and Homotopy -- I*-Measure of a Homogeneous Space -- The Cartan Theorem -- Effective Computation and Axiomatic System of I*-Measure -- I*-Measures Connected with Fibrations -- Bibliography -- Index.

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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.

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