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Strong Shape and Homology

  • Book
  • © 2000

Overview

Authors:
  1. Sibe Mardešić

    1. Department of Mathematics, University of Zagreb, Zagreb, Croatia

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  • Shape theory was introduced by Borsuk 30 years ago and Mardesic contributed greatly to it.
  • One expert says: "If we need a book in the field, this is it!
  • It is thorough, careful and complete."
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (23 chapters)

  1. Front Matter

    Pages I-XII
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  2. Introduction

    1. Introduction

      • Sibe Mardešić
      Pages 1-5

  3. Coherent Homotopy

    1. Front Matter

      Pages 7-7
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    2. Coherent mappings

      • Sibe Mardešić
      Pages 9-27

    3. Coherent homotopy

      • Sibe Mardešić
      Pages 29-46

    4. Coherent homotopy of sequences

      • Sibe Mardešić
      Pages 47-60

    5. Coherent homotopy and localization

      • Sibe Mardešić
      Pages 61-91

    6. Coherent homotopy as a Kleisli category

      • Sibe Mardešić
      Pages 93-100

  4. Strong Shape

    1. Front Matter

      Pages 101-101
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    2. Resolutions

      • Sibe Mardešić
      Pages 103-127

    3. Strong expansions

      • Sibe Mardešić
      Pages 129-145

    4. Strong shape

      • Sibe Mardešić
      Pages 147-180

    5. Strong shape of metric compacta

      • Sibe Mardešić
      Pages 181-199

    6. Selected results on strong shape

      • Sibe Mardešić
      Pages 201-212

  5. Higher Derived Limits

    1. Front Matter

      Pages 213-213
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    2. The derived functors of lim

      • Sibe Mardešić
      Pages 215-252

    3. limn and the extension functors Extn

      • Sibe Mardešić
      Pages 253-268

    4. The vanishing theorems

      • Sibe Mardešić
      Pages 269-283

    5. The cofinality theorem

      • Sibe Mardešić
      Pages 285-300

    6. Higher limits on the category pro — Mod

      • Sibe Mardešić
      Pages 301-316
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Keywords

About this book

Shape theory is an extension of homotopy theory from the realm of CW-complexes to arbitrary spaces. Besides applications in topology, it has interesting applications in various other areas of mathematics, especially in dynamical systems and C*-algebras. Strong shape is a refinement of ordinary shape with distinct advantages over the latter. Strong homology generalizes Steenrod homology and is an invariant of strong shape. The book gives a detailed account based on approximation of spaces by polyhedra (ANR's) using the technique of inverse systems. It is intended for researchers and graduate students. Special care is devoted to motivation and bibliographic notes.

Authors and Affiliations

  • Department of Mathematics, University of Zagreb, Zagreb, Croatia

    Sibe Mardešić

Bibliographic Information

  • Book Title: Strong Shape and Homology

  • Authors: Sibe Mardešić

  • Series Title: Springer Monographs in Mathematics

  • DOI: https://doi.org/10.1007/978-3-662-13064-3

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 2000

  • Hardcover ISBN: 978-3-540-66198-6Published: 22 November 1999

  • Softcover ISBN: 978-3-642-08546-8Published: 15 December 2010

  • eBook ISBN: 978-3-662-13064-3Published: 14 March 2013

  • Series ISSN: 1439-7382

  • Series E-ISSN: 2196-9922

  • Edition Number: 1

  • Number of Pages: XII, 489

  • Topics: Algebraic Topology, Mathematics, general, Algebra, K-Theory

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