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Mathematical Modeling Through Topological Surgery and Applications

  • Stathis Antoniou

Part of the Springer Theses book series (Springer Theses)

Table of contents

  1. Front Matter
    Pages i-xvii
  2. Stathis Antoniou
    Pages 1-3
  3. Stathis Antoniou
    Pages 5-14
  4. Stathis Antoniou
    Pages 15-19
  5. Stathis Antoniou
    Pages 21-23
  6. Stathis Antoniou
    Pages 25-32
  7. Stathis Antoniou
    Pages 33-40
  8. Stathis Antoniou
    Pages 49-55
  9. Stathis Antoniou
    Pages 57-65
  10. Stathis Antoniou
    Pages 67-77
  11. Stathis Antoniou
    Pages 79-80
  12. Back Matter
    Pages 81-85

About this book

Introduction

Topological surgery is a mathematical technique used for creating new manifolds out of known ones. In this book the authors observe that it also occurs in natural phenomena of all scales: 1-dimensional surgery happens during DNA recombination and when cosmic magnetic lines reconnect; 2-dimensional surgery happens during tornado formation and cell mitosis; and they conjecture that 3-dimensional surgery happens during the formation of black holes from cosmic strings, offering an explanation for the existence of a black hole’s singularity. Inspired by such phenomena, the authors present a new topological model that extends the formal definition to a continuous process caused by local forces. Lastly, they describe an intrinsic connection between topological surgery and a chaotic dynamical system exhibiting a “hole drilling” behavior. The authors’ model indicates where to look for the forces causing surgery and what deformations should be observed in the local submanifolds involved. These predictions are significant for the study of phenomena exhibiting surgery and they also open new research directions. This novel study enables readers to gain a better understanding of the topology and dynamics of various natural phenomena, as well as topological surgery itself and serves as a basis for many more insightful observations and new physical implications.

Keywords

Mathematical Surgery Natural Occurring Topological Surgery Chaotic Dynamical Systems Reconnection and Topological Drilling Black Holes and Topological Surgery Nested Tori Falaco Solitons Cosmic Strings

Authors and affiliations

  • Stathis Antoniou
    • 1
  1. 1.School of Applied Mathematical and Physical Sciences, Department of MathematicsNational Technical University of AthensAthensGreece

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-97067-7
  • Copyright Information Springer Nature Switzerland AG 2018
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-97066-0
  • Online ISBN 978-3-319-97067-7
  • Series Print ISSN 2190-5053
  • Series Online ISSN 2190-5061
  • Buy this book on publisher's site