MAT553 Poly 2014-2015.pdfMAT553 Poly 2014-2015.pdf

Differentiable manifolds are geometric objects, locally parametrized by coordinate systems, but with a global topology that can be nontrivial. They are therefore the natural language of differential geometry (Riemannian, symplectic, complex, etc...), and also of many physical theories (general relativity, gauge theory, etc...).

The goal of this course is to provide an introduction to manifolds, and to a number of related key concepts: smooth maps between manifolds, vector bundles, transversality, intersection theory, Morse Theory, differential forms and integration, connexions, parallel transport, metric and curvature.