Topology of Riemann Surfaces

Related lectures (31)

Page 2 of 4

Covers the normalization process of plane algebraic curves, focusing on irreducible polynomials and affine curves.

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

Explores curves with Poritsky property, Birkhoff integrability, and Liouville nets in billiards.

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

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

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

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

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

Covers modular curves as compact Riemann surfaces, explaining their topology, construction of holomorphic charts, and properties.

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