Geometry in Physics
by Alexander Altland
Number of pages: 79
From the table of contents: Exterior Calculus (Exterior Algebra, Differential forms in Rn, Metric, Gauge theory, Summary and outlook); Manifolds (Basic structures, Tangent space, Summary and outlook); Lie groups (Generalities, Lie group actions, Lie algebras, Lie algebra actions, From Lie algebras to Lie groups).
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by Maximilian Kreuzer - Technische Universitat Wien
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.
by Dominic Joyce - arXiv
An introduction to Calabi-Yau manifolds and special Lagrangian submanifolds from the differential geometric point of view, followed by recent results on singularities of special Lagrangian submanifolds, and their application to the SYZ Conjecture.
by Shahn Majid - arXiv
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.
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.