Haken manifold

Related lectures (31)

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Explores matrix-based and matrix-free approaches for computing the Newton step in optimization on manifolds.

Introduces d-dimensional charts on manifolds and the concept of an atlas.

Covers the topology of Riemann surfaces, focusing on orientation and orientability.

Covers retractions, tangent bundles, and embedded submanifolds on manifolds with proofs and examples.

Explores conformal symmetries in Euclidean and AdS spaces, isometries, induced metric, Poincaré coordinates, and boundary structure.

Explores Taylor expansions of first order in optimization on manifolds.

Covers smooth sets and functions on manifolds, with a focus on constructing an atlas for a circle.

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

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

Explores connections on manifolds, emphasizing the axiomatic definition and properties of derivatives in differentiating vector fields.