Analysis on Manifolds

Manifolds, manifolds with boundary, orientable manifolds. Partition of unity. Application: Whitney embedding’s theorem for compact manifolds. Tangent and cotangent bundles. Differentiable mappings, regular values. Skew-symmetric forms, differential forms, exterior differential. Surface Integrals. Stokes’ theorem. De Rham cohomology. Mayer-Vietoris sequence. Invariance by homotopy. Applications.

References:
LIMA, E.L. – Curso de Análise – Vol. 2. Rio de Janeiro, IMPA, Projeto Euclides, 1989.
LIMA, E.L. – Homologia básica. Rio de Janeiro, IMPA, Projeto Euclides, 2009.
SPIVAK, M. – Calculus on Manifolds. New York. Benjamin, 1965.
TU, L. W. – An introduction to manifolds. Universitext. Springer, New York, 2008.

* Standard program. The teacher has the autonomy to make any changes.