Sumários
Inital submanifolds, embeddings and Whitney's Theorem
24 setembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
Definition of initial submanifold. Example. Definition of regular and singular points and regular and singular values. Definition of transversality. Embbeded submanifolds. Whitney's Theorem.
Tangent space and the differential. Immersions, submersions and submanifolds.
18 setembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
Definition of tangent vector, tangent and cotangent spaces and the differential of a smooth function. Tangent bundle and cotangent bundle. Definition of immersion, submersion, submanifold, embedding and embedded submanifold. Local normal form for immersed and embedded submanifolds. Equivalent submanifolds.
Smooth manifolds
17 setembro 2018, 11:00 • Sílvia Nogueira da Rocha Ravasco dos Anjos
Smooth manifold: topological space M of dimension d, Hausdorff and second countable with a maximal atlas (smooth structure). Diffeomorphisms and equivalent smooth structures. Definition and existence of partitions of unity.