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Computational Homology

  • Tomasz Kaczynski
  • Konstantin Mischaikow
  • Marian Mrozek

Part of the Applied Mathematical Sciences book series (AMS, volume 157)

Table of contents

  1. Front Matter
    Pages I-XVII
  2. Homology

    1. Front Matter
      Pages 1-1
    2. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 3-37
    3. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 39-92
    4. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 93-141
    5. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 143-171
    6. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 173-197
    7. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 199-234
    8. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 235-254
  3. Extensions

    1. Front Matter
      Pages 255-255
    2. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 257-278
    3. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 279-306
    4. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 307-376
    5. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 377-393
  4. Tools from Topology and Algebra

    1. Front Matter
      Pages 395-395
    2. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 397-418
    3. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 419-449
    4. Tomasz Kaczynski, Konstantin Mischaikow, Marian Mrozek
      Pages 451-464
  5. Back Matter
    Pages 465-482

About this book

Introduction

In recent years, there has been a growing interest in applying homology to problems involving geometric data sets, whether obtained from physical measurements or generated through numerical simulations. This book presents a novel approach to homology that emphasizes the development of efficient algorithms for computation.

As well as providing a highly accessible introduction to the mathematical theory, the authors describe a variety of potential applications of homology in fields such as digital image processing and nonlinear dynamics. The material is aimed at a broad audience of engineers, computer scientists, nonlinear scientists, and applied mathematicians.

Mathematical prerequisites have been kept to a minimum and there are numerous examples and exercises throughout the text. The book is complemented by a website containing software programs and projects that help to further illustrate the material described within.

Keywords

Algebraic topology Homotopy Lefschetz fixed-point theorem algorithms fixed-point theorem homological algebra homology nonlinear dynamics

Authors and affiliations

  • Tomasz Kaczynski
    • 1
  • Konstantin Mischaikow
    • 2
  • Marian Mrozek
    • 3
  1. 1.Department of Mathematics and Computer ScienceUniversity of SherbrookeQuebecCanada
  2. 2.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA
  3. 3.Institute of Computer ScienceJagiellonian UniversityKrakówPoland

Bibliographic information

  • DOI https://doi.org/10.1007/b97315
  • Copyright Information Springer Science+Business Media New York 2004
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-2354-7
  • Online ISBN 978-0-387-21597-6
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site