Introduction to Braided Geometry and q-Minkowski Space
by Shahn Majid
Publisher: arXiv 1994
Number of pages: 60
We present a systematic introduction to the geometry of linear braided spaces. These are versions of Rn in which the coordinates xi have braid-statistics described by an R-matrix. From this starting point we survey the author's braided-approach to q-deformation.
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by Gabriel Lugo - University of North Carolina at Wilmington
These notes were developed as a supplement to a course on Differential Geometry at the advanced undergraduate level, which the author has taught. This texts has an early introduction to differential forms and their applications to Physics.
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Both dynamical systems and symplectic geometry have rich theories and the time seems ripe to develop the common core with integrated ideas from both fields. We discuss problems which show how dynamical systems and symplectic ideas come together.
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An introduction to the ideas of microlocal analysis and the related symplectic geometry, with an emphasis on the role which these ideas play in formalizing the transition between the mathematics of classical dynamics and that of quantum mechanics.
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From the table of contents: Topology (Homotopy, Manifolds, Surfaces, Homology, Intersection numbers and the mapping class group); Differentiable manifolds; Riemannian geometry; Vector bundles; Lie algebras and representations; Complex manifolds.