The Geometrization of Physics
by Richard S. Palais
Publisher: University of California at Irvine 1981
Number of pages: 107
The major goal of these notes is to develop, in sufficient detail to be convincing, an observation that basically goes back to Kaluza and Klein in the early 1920's that not only can gauge fields of the "Yang-Mills" type be unified with the remarkable successful Einstein model of gravitation in a beautiful, simple, and natural manner, but also that when this unification is made they, like gravitational field, disappear as forces and are described by pure geometry, in the sense that particles simply move along geodesics of an appropriate Riemannian geometry.
Home page url
Download or read it online for free here:
by Barney Bramham, Helmut Hofer - arXiv
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.
by Vincent Bouchard - arXiv
These are introductory lecture notes on complex geometry, Calabi-Yau manifolds and toric geometry. We first define basic concepts of complex and Kahler geometry. We then proceed with an analysis of various definitions of Calabi-Yau manifolds.
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.