04001nam a22006375i 4500 978-3-031-59501-1 DE-He213 20251030113044.0 cr nn 008mamaa 240916s2024 sz | s |||| 0|eng d 9783031595011 978-3-031-59501-1 10.1007/978-3-031-59501-1 doi QC19.2-20.85 PHU bicssc SCI040000 bisacsh PHU thema Govindarajan, T. R. author. aut http://id.loc.gov/vocabulary/relators/aut 84340 Geometry and Topology of Low Dimensional Systems [electronic resource] : Chern-Simons Theory with Applications / by T. R. Govindarajan, Pichai Ramadevi. 1st ed. 2024. Cham : Springer International Publishing : Imprint: Springer, 2024. XIV, 167 p. 48 illus., 9 illus. in color. online resource. text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Lecture Notes in Physics, 1616-6361 ; 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. Mathematical physics. Topology. 72917 Elementary particles (Physics). 68885 Quantum field theory. 68886 Topological groups. 72299 Lie groups. 72300 Associative rings. 72027 Associative algebras. 72028 Mathematical Physics. Topology. 72917 Elementary Particles, Quantum Field Theory. 68887 Topological Groups and Lie Groups. 72304 Associative Rings and Algebras. 72029 Ramadevi, Pichai. author. aut http://id.loc.gov/vocabulary/relators/aut 84341 SpringerLink (Online service) Springer Nature eBook Printed edition: 9783031595004 Printed edition: 9783031595028 Lecture Notes in Physics, 1616-6361 ; 1027 72070 https://doi.org/10.1007/978-3-031-59501-1 ZDB-2-PHA ZDB-2-SXP ZDB-2-LNP 63402 63402