Surface Classification

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Related lectures (29)

Page 1 of 3

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

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.

Holomorphic Functions: Taylor Series Expansion

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

Hamiltonian Homeomorphisms on Surfaces

Explores the action of Hamiltonian homeomorphisms on surfaces and discusses related mathematical concepts.

Real Surfaces: Defects and Reconstructions

Explores the difference between ideal and real surfaces, defects, and surface reconstructions.

Topology of Riemann Surfaces

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

Fundamental Groups

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

Open Mapping Theorem

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

Building surfaces from equilateral triangles

Explores the construction of Riemann surfaces from equilateral triangles and the dynamics of finite-type maps.

Meromorphic Functions & Differentials

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