Differentiable Manifolds


Differentiable manifolds: local structure, submanifolds, Sard's Theorem, transversality, vector fields and flows. Fibre bundles, tangent and cotangent bundles of a manifold. Lie derivative of vector fields. Lie algebras. Lie groups (classical). Homogeneous spaces. Differential forms, exterior derivative. Symplectic forms. Integration on manifolds. Stokes' theorem. One or more of the following additional topics may also be covered:
- Riemannian manifolds. Curvature. Symmetric spaces. Classical examples.
- de Rham cohomology, singular cohomology and de Rham's theorem.
- Degree of a map. Index of a vector field. Applications.
- Distributions. Frobenius and Stefan-Sussmann theorems.

Research and Events


  • Research Seminar Program (RSP)
    2017/18 second session
    Room 2.5, DMat UC
    March 9, 2018
  • PhD Defense
    Muhammad Ali Khan - Statistical instability in chaotic dynamics
    Room 031, Dep. Mathematics, Univ. Porto
    March 9, 2018
  • PhD Defense
    Anderson Feitoza Leitão Maia - Sharp regularity for the inhomogeneous porous medium equation
    14:30 - Sala dos Capelos, Univ. Coimbra
    March 21, 2018
More Events

Defended Theses

  • Forward-backward stochastic differential equations and applications
      Rui Manuel Tavares Pinto de Sá Pereira (January 2018)
      Evelina Shamarova
      Margarida Brito
  • Pseudomonads and descent
      Fernando Lucatelli Nunes (January 2018)
      Maria Manuel Clementino
  • Descent theory of (T,V)-categories: global-descent and étale-descent
      Pier Giorgio Basile (September 2017)
      Maria Manuel Clementino
More Theses