3-manifold

Related lectures (31)

Explores pseudorandomness theory, AI challenges, pseudo-random graphs, random walks, and matrix properties.

Explores smooth maps, differentials, composition properties, linearity, and extensions on manifolds.

Introduces manifolds, charts, atlases, tangent space, tensors, and the metric in curved spaces.

Explores the dynamics of singular Riemann surface foliations near singular points and their relation to compact manifolds.

Delves into Topological Data Analysis, exploring the shape of data and its underlying structure through mathematical tools and concepts.

Explores flow projection on stable and unstable manifolds using dual basis and Gram-Schmidt, with practical error quantification.

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

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

Covers the concept of orientation and degrees in topology, focusing on assigning orientations to manifolds.

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

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

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