Manifolds

Related lectures (27)

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Explores Schottky groups, spectral gaps, and the Fractal Uncertainty Principle.

Explores the connected sum of surfaces, focusing on torus and RP2, highlighting the resulting homeomorphism with the sphere.

Explores sphere properties, projections, and symmetry, including apparent contours and missing projections of points.

Covers the Riemann sphere, focusing on its conditions and correlation functions in mathematical and physical contexts.

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

Delves into cell attachment, exploring its implications for different cell dimensions.

Introduces hyperbolic geometry, covering complete metric spaces, isometries, and Gaussian curvature in dimension 2.

Explores the intersection of a sphere, cone, and paraboloid in 3D space.

Explores the intrinsic geometry of regular surfaces and isometric transformations, including spheres and cylinders.

Covers the integration of differential forms on smooth manifolds, including the concepts of closed and exact forms.