Lectures related to Topology: Fundamental Groups and Applications

Introduces metric spaces, topology, and continuity, emphasizing the importance of open sets and the Hausdorff property.

Covers the definition and examples of topological groups, focusing on actions of groups on spaces.

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

Covers homotopy, quotient spaces, and the universal property in topology.

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

Covers commutative diagrams, homotopy, and constructing topological spaces.

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

Introduces the homotopy category of a model category with inverted weak equivalences and unique homotopy equivalences.

Introduces the homotopy extension property, exploring conditions for extending continuous maps.