Atlas (topology)

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Related lectures (12)

Fundamental Groups

Explores fundamental groups, homotopy classes, and coverings in connected manifolds.

Local Homeomorphisms and Coverings

Covers the concepts of local homeomorphisms and coverings in manifolds, emphasizing the conditions under which a map is considered a local homeomorphism or a covering.

Topology of Riemann Surfaces

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

Smooth sets and functions: Smooth functions, topology, and manifolds

Explores smooth functions on manifolds, emphasizing continuity and atlas topologies.

Differential Forms on Manifolds

Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.

Harmonic Forms: Main Theorem

Explores harmonic forms on Riemann surfaces and the uniqueness of solutions to harmonic equations.

Riemann Surfaces: Complex Manifolds

Covers Riemann surfaces as complex manifolds of dimension 1, including transition maps and holomorphic functions.

Differentiating Vector Fields: Definition

Introduces differentiating vector fields along curves on manifolds with connections and the unique operator satisfying specific properties.

TNB Frame: Frenet-Serret Formulas

Covers the TNB frame and Frenet-Serret formulas for understanding curve behavior.

Smooth sets and functions: Charts and atlases

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

Harmonic Forms and Riemann Surfaces

Explores harmonic forms on Riemann surfaces, covering uniqueness of solutions and the Riemann bilinear identity.

General Manifolds and Topology

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

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