Local structure of totally disconnected locally compact groups V

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Subsets and subgroups associated with an action

Explores subsets, subgroups, actions, fixed points, stabilizers, orbits, and bijections in group theory.

Cohomology: Cross Product

Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.

Jordan Curve Theorem

Covers the proof of the Jordan Curve Theorem and the properties of embedded spheres.

Proof of Weyl's Theorem

Explores the proof of Weyl's theorem, focusing on discrete spectrum, ground states, and potential energy continuity.

Topology of Riemann Surfaces

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

Group Actions: Quotients and Homomorphisms

Discusses group actions, quotients, and homomorphisms, emphasizing practical implications for various groups and the construction of complex projective spaces.

Joint Equidistribution of CM Points

Covers the joint equidistribution of CM points and the ergodic decomposition theorem in compact abelian groups.

Cantor-Heine Theorem

Covers the Cantor-Heine theorem, discussing uniform continuity and compactness.

Optimal Transport: Convexity and Inequalities

Explores optimal transport, emphasizing convexity properties and inequalities in compact sets.

Bar Construction: Homology Groups and Classifying Space

Covers the bar construction method, homology groups, classifying space, and the Hopf formula.