Mathematical Modeling Through Topological Surgery and Applications

• Main Author: Antoniou, Stathis (Author, http://id.loc.gov/vocabulary/relators/aut)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2018.
• Edition: 1st ed. 2018.
• Series: Springer Theses, Recognizing Outstanding Ph.D. Research,
• Subjects: Physics.; Topology.; Cosmology.; Statistical physics.; Dynamics.; Ergodic theory.; Mathematical Methods in Physics.; Statistical Physics and Dynamical Systems.; Dynamical Systems and Ergodic Theory.

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 s...

Table of Contents:

• Introduction
• Useful Mathematical Notions
• The Formal Definition of Surgery
• Continuity
• Dynamics
• Solid Surgery
• A Dynamical System Modeling Solid 2-Dimensional 0-Surgery
• The Ambient Space S3
• Embedded Surgery
• 3-Dimensional Surgery
• Conclusions.