From embedded to general manifolds: upgrading our foundations

Related lectures (33)

Delves into topological entropy in compact manifolds and Reeb flows, emphasizing the forcing of entropy via cylindrical contact homology.

Explores smooth functions, n-dimensional charts, compatibility, and atlases for manifolds.

Covers manifolds, topology, smooth maps, and tangent vectors in detail.

Covers smooth maps on manifolds, defining functions, tangent spaces, and differentials.

Explores the definition of connections for smooth vector fields on manifolds.

Explores Riemannian connections on manifolds, emphasizing smoothness and compatibility with the metric.

Covers optimization on manifolds, focusing on smooth manifolds and functions, and the process of gradient descent.

Introduces Manopt, a toolbox for optimization on manifolds, focusing on solving optimization problems on smooth manifolds using the Matlab version.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Covers embedded submanifolds, Stiefel manifold, tangent spaces, and differential ranks.

Covers the definition of retraction, open submanifolds, local defining functions, tangent spaces, and Riemannian metrics.

Covers smooth maps, vector fields, and retractions on manifolds, emphasizing the importance of smoothly varying curves.

Covers the parameterization of curves, tangent and normal vectors, simple closed curves, exterior normal, regular curves, and domains in R^2.

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