Sumários
Computations in Cohomology (cont.)
13 novembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
Euler characteristic. Euler's formula. Poincaré duality and its corollaries.
Computations in Cohomology
12 novembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
Example: computation of the cohomology of the sphere of dimension d.
Homotopy invariance (cont.) The Mayer-Vietoris sequence.
6 novembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
Homotopy invariance. Manifolds with the same homotopy type and contractible manifolds. Examples.
Homotopy invariance
5 novembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
The compactly supported de Rham complex and its cohomology, an invariant of differentiable manifolds.
Integration of Differential forms. De Rham cohomology.
30 outubro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
The Lie derivative and the Cartan's magic formula. Volume forms and orientable manifolds. The Frobenius Theorem in the language of differential forms.
Integration of differential forms on manifolds and Stokes Theorem. The de Rham complex and its cohomology, important invariant of differentiable manifolds.