Closed Curves and Topological Spaces

Related lectures (32)

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

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

Covers induced homomorphisms on relative homology groups and their properties.

Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.

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

Explores the application of the Gauss/Green theorem to calculate curve integrals along simple closed curves.

Explores the Intermediate Values Theorem for continuous functions on closed intervals.

Explores curvature, inflection points, and angular functions in plane curves, highlighting the importance of inflection points.

Covers manifolds, charts, compatibility, and submanifolds with smooth analytic equations.

Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.