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Geometry and topology of low dimensi...

Govindarajan, T. R.

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Geometry and topology of low dimensional systems = Chern-Simons theory with applications /

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Geometry and topology of low dimensional systems/ by T. R. Govindarajan, Pichai Ramadevi.
其他題名:	Chern-Simons theory with applications /
作者:	Govindarajan, T. R.
其他作者:	Ramadevi, Pichai.
出版者:	Cham :Springer International Publishing : : 2024.,
面頁冊數:	xiv, 167 p. :ill. (some col.), digital ;24 cm.
內容註:	Introduction -- Differentiable Manifolds and Geometry -- Riemannian and Pseudo Riemannian Geometry -- Topological Understanding of Defects in Crystalline Structure -- Configuration Space Topology and Topological Conservation Laws -- Spin Statistics Theorem, and Low Dimensional Geometry and Topology -- Braid Group, Knots, Three Manifolds -- Chern-Simons Field Theory -- 3D Gravity as Topological Quantum Field Theory.
Contained By:	Springer Nature eBook
標題:	Low-dimensional topology. -
電子資源:	https://doi.org/10.1007/978-3-031-59501-1
ISBN:	9783031595011

Geometry and topology of low dimensional systems = Chern-Simons theory with applications /
Govindarajan, T. R.

Geometry and topology of low dimensional systemsChern-Simons theory with applications /[electronic resource] :by T. R. Govindarajan, Pichai Ramadevi. - Cham :Springer International Publishing :2024. - xiv, 167 p. :ill. (some col.), digital ;24 cm. - Lecture notes in physics,v. 10271616-6361 ;. - Lecture notes in physics ;v. 1027..

Introduction -- Differentiable Manifolds and Geometry -- Riemannian and Pseudo Riemannian Geometry -- Topological Understanding of Defects in Crystalline Structure -- Configuration Space Topology and Topological Conservation Laws -- Spin Statistics Theorem, and Low Dimensional Geometry and Topology -- Braid Group, Knots, Three Manifolds -- Chern-Simons Field Theory -- 3D Gravity as Topological Quantum Field Theory.

This book introduces the field of topology, a branch of mathematics that explores the properties of geometric space, with a focus on low-dimensional systems. The authors discuss applications in various areas of physics. The first chapters of the book cover the formal aspects of topology, including classes, homotopic groups, metric spaces, and Riemannian and pseudo-Riemannian geometry. These topics are essential for understanding the theoretical concepts and notations used in the next chapters of the book. The applications encompass defects in crystalline structures, space topology, spin statistics, Braid group, Chern-Simons field theory, and 3D gravity, among others. This self-contained book provides all the necessary additional material for both physics and mathematics students. The presentation is enriched with examples and exercises, making it accessible for readers to grasp the concepts with ease. The authors adopt a pedagogical approach, posing many unsolved questions in simple situations that can serve as challenging projects for students. Suitable for a one-semester postgraduate level course, this text is ideal for teaching purposes.

ISBN: 9783031595011

Standard No.: 10.1007/978-3-031-59501-1doiSubjects--Topical Terms:

659140
Low-dimensional topology.

LC Class. No.: QA612.14

Dewey Class. No.: 514.2

Geometry and topology of low dimensional systems = Chern-Simons theory with applications /
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505 0 $a Introduction -- Differentiable Manifolds and Geometry -- Riemannian and Pseudo Riemannian Geometry -- Topological Understanding of Defects in Crystalline Structure -- Configuration Space Topology and Topological Conservation Laws -- Spin Statistics Theorem, and Low Dimensional Geometry and Topology -- Braid Group, Knots, Three Manifolds -- Chern-Simons Field Theory -- 3D Gravity as Topological Quantum Field Theory.
520 $a This book introduces the field of topology, a branch of mathematics that explores the properties of geometric space, with a focus on low-dimensional systems. The authors discuss applications in various areas of physics. The first chapters of the book cover the formal aspects of topology, including classes, homotopic groups, metric spaces, and Riemannian and pseudo-Riemannian geometry. These topics are essential for understanding the theoretical concepts and notations used in the next chapters of the book. The applications encompass defects in crystalline structures, space topology, spin statistics, Braid group, Chern-Simons field theory, and 3D gravity, among others. This self-contained book provides all the necessary additional material for both physics and mathematics students. The presentation is enriched with examples and exercises, making it accessible for readers to grasp the concepts with ease. The authors adopt a pedagogical approach, posing many unsolved questions in simple situations that can serve as challenging projects for students. Suitable for a one-semester postgraduate level course, this text is ideal for teaching purposes.
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650 2 4 $a Elementary Particles, Quantum Field Theory. $3 894026
650 2 4 $a Topological Groups and Lie Groups. $3 3593340
650 2 4 $a Associative Rings and Algebras. $3 897405
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