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 Alexander Altland
Contents: Exterior Calculus (Exterior Algebra, Differential forms in Rn, Metric, Gauge theory); Manifolds (Basic structures, Tangent space); Lie groups (Lie group actions, Lie algebras, Lie algebra actions, From Lie algebras to Lie groups).
by C. Nash - arXiv
In this essay we wish to embark on the telling of a story which, almost certainly, stands only at its beginning. We shall discuss the links and the interaction between one very old subject, physics, and a much newer one, topology.
by Richard S. Palais - University of California at Irvine
The major goal of these notes is to develop an observation that not only can gauge fields of the Yang-Mills type be unified with the Einstein model of gravitation, but also that when this unification is made they are described by pure geometry.
by Sean Bates, Alan Weinstein - University of California at Berkeley
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.