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 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 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 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 Giovanni Landi - arXiv
These lectures notes are an introduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists.