Topology: Fundamental Groups and Surfaces

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Related lectures (30)

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Topology: Open Sets, Compactness, and Connectivity

Explores open sets, compactness, and connectivity in topology, covering topological spaces and compact sets.

Homotopy Classes

Covers the concept of homotopy classes and their properties in topology, including short components and group concatenation.

Relative Homotopy Groups

Covers relative homotopy groups, establishing long exact sequences and defining boundary homomorphisms.

Topological Waves for Robust Signal Processing Applications

Explores topological waves for robust signal processing applications, focusing on resistance to perturbations and the design paradigm of topological systems.

Homotopy and Quotient Spaces

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

Topological Groups

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

Modular curves: Riemann surfaces and transition maps

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

Group Actions and Fundamental Groups

Delves into group actions, coverings, fundamental groups, and homomorphisms in topological spaces.

Local structure of totally disconnected locally compact groups I

Covers the local structure of totally disconnected locally compact groups, exploring properties and applications.

Cell Attachment and Homotopy

Covers cell attachment, homotopy, mappings, and universal properties in topology.