Local Homeomorphisms and Coverings

Related lectures (31)

Page 1 of 4

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

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

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

Covers the topology of Riemann surfaces and the concept of triangulation using finitely many triangles.

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

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

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

Covers proper actions of groups on Riemann surfaces and introduces algebraic curves via square roots.

Explores meromorphic functions, poles, residues, orders, divisors, and the Riemann-Roch theorem.