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020 _a9783031595011
_9978-3-031-59501-1
024 7 _a10.1007/978-3-031-59501-1
_2doi
050 4 _aQC19.2-20.85
072 7 _aPHU
_2bicssc
072 7 _aSCI040000
_2bisacsh
072 7 _aPHU
_2thema
100 1 _aGovindarajan, T. R.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984340
245 1 0 _aGeometry and Topology of Low Dimensional Systems
_h[electronic resource] :
_bChern-Simons Theory with Applications /
_cby T. R. Govindarajan, Pichai Ramadevi.
250 _a1st ed. 2024.
264 1 _aCham :
_bSpringer International Publishing :
_bImprint: Springer,
_c2024.
300 _aXIV, 167 p. 48 illus., 9 illus. in color.
_bonline resource.
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
347 _atext file
_bPDF
_2rda
490 1 _aLecture Notes in Physics,
_x1616-6361 ;
_v1027
505 0 _aIntroduction -- 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 _aThis 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.
650 0 _aMathematical physics.
650 0 _aTopology.
_972917
650 0 _aElementary particles (Physics).
_968885
650 0 _aQuantum field theory.
_968886
650 0 _aTopological groups.
_972299
650 0 _aLie groups.
_972300
650 0 _aAssociative rings.
_972027
650 0 _aAssociative algebras.
_972028
650 1 4 _aMathematical Physics.
650 2 4 _aTopology.
_972917
650 2 4 _aElementary Particles, Quantum Field Theory.
_968887
650 2 4 _aTopological Groups and Lie Groups.
_972304
650 2 4 _aAssociative Rings and Algebras.
_972029
700 1 _aRamadevi, Pichai.
_eauthor.
_4aut
_4http://id.loc.gov/vocabulary/relators/aut
_984341
710 2 _aSpringerLink (Online service)
773 0 _tSpringer Nature eBook
776 0 8 _iPrinted edition:
_z9783031595004
776 0 8 _iPrinted edition:
_z9783031595028
830 0 _aLecture Notes in Physics,
_x1616-6361 ;
_v1027
_972070
856 4 0 _uhttps://doi.org/10.1007/978-3-031-59501-1
912 _aZDB-2-PHA
912 _aZDB-2-SXP
912 _aZDB-2-LNP
999 _c63402
_d63402