Authors:
- Nominated as an outstanding Ph.D thesis by the National Technical University of Athens, Greece
- Details how topological surgery is exhibited in nature
- Provides a topological perspective on the formation of black holes
- Connects topological surgery with dynamical systems
Part of the book series: Springer Theses (Springer Theses)
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Table of contents (11 chapters)
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Front Matter
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Back Matter
About this book
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.
Authors and Affiliations
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School of Applied Mathematical and Physical Sciences, Department of Mathematics, National Technical University of Athens, Athens, Greece
Stathis Antoniou
About the author
Stathis Antoniou received his PhD in 2018. His research interests include low-dimensional topology and mathematical modeling. He has worked in the private sector in data analytics and is currently doing research on topological surgery, Morse theory and cosmological phenomena.
Bibliographic Information
Book Title: Mathematical Modeling Through Topological Surgery and Applications
Authors: Stathis Antoniou
Series Title: Springer Theses
DOI: https://doi.org/10.1007/978-3-319-97067-7
Publisher: Springer Cham
eBook Packages: Physics and Astronomy, Physics and Astronomy (R0)
Copyright Information: Springer Nature Switzerland AG 2018
Hardcover ISBN: 978-3-319-97066-0Published: 31 August 2018
Softcover ISBN: 978-3-030-07297-1Published: 19 January 2019
eBook ISBN: 978-3-319-97067-7Published: 23 August 2018
Series ISSN: 2190-5053
Series E-ISSN: 2190-5061
Edition Number: 1
Number of Pages: XVII, 85
Number of Illustrations: 10 b/w illustrations, 27 illustrations in colour
Topics: Mathematical Methods in Physics, Topology, Cosmology, Statistical Physics and Dynamical Systems, Dynamical Systems and Ergodic Theory