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Mathematical modeling through topolo...

Antoniou, Stathis.

Mathematical modeling through topological surgery and applications

Record Type:	Electronic resources : Monograph/item
Title/Author:	Mathematical modeling through topological surgery and applicationsby Stathis Antoniou.
Author:	Antoniou, Stathis.
Published:	Cham :Springer International Publishing :2018.
Description:	xvii, 85 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Topological manifolds.
Online resource:	http://dx.doi.org/10.1007/978-3-319-97067-7
ISBN:	9783319970677$q(electronic bk.)

Mathematical modeling through topological surgery and applications
Antoniou, Stathis.

Mathematical modeling through topological surgery and applications[electronic resource] /by Stathis Antoniou. - Cham :Springer International Publishing :2018. - xvii, 85 p. :ill., digital ;24 cm. - Springer theses,2190-5053. - Springer theses..

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.

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.

ISBN: 9783319970677$q(electronic bk.)

Standard No.: 10.1007/978-3-319-97067-7doiSubjects--Topical Terms:

205883
Topological manifolds.

LC Class. No.: QA613.2 / .A586 2018

Dewey Class. No.: 514.34

Mathematical modeling through topological surgery and applications
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100 1 $a Antoniou, Stathis. $3 822574
245 1 0 $a Mathematical modeling through topological surgery and applications $h [electronic resource] / $c by Stathis Antoniou.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2018.
300 $a xvii, 85 p. : $b ill., digital ; $c 24 cm.
490 1 $a Springer theses, $x 2190-5053
505 0 $a 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.
520 $a 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.
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650 2 4 $a Dynamical Systems and Ergodic Theory. $3 273794
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