Concept

Covering group

Related lectures (32)

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

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.

Bounding the Poisson bracket invariant on surfaces

Covers the concept of bounding the Poisson bracket invariant on surfaces, exploring joint work with A. Logunov and S. Tanny.

Student Feedback and Topology Concepts

Covers student feedback, group exercises, and fundamental topology concepts, emphasizing the importance of understanding coverings and group actions.

Universal Covering Construction

Introduces the concept of a universal covering construction with examples like Hawaiian rings.

Heisenberg Group: Representation

Covers the Heisenberg group representation, including shifts, multiplications, and the Fourier transform, extending to finite fields and metaplectic groups.

Lifting Criterion

Explores the lifting criterion for maps between path-connected and locally path-connected spaces.

Path Lifting

Explores path lifting, homotopy properties, and homomorphisms in covering spaces.

Group Actions and Fundamental Groups

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

Categorical Perspective: Abelian Groups

Explores abelian groups from a categorical perspective, discussing the coproduct construction.

Groupes Isomorphes: Applications

Explores isomorphic groups, bijective morphisms, and their applications in group theory.

Group Actions on Sets

Explores group actions on sets through homomorphisms and Cartesian products, illustrating their properties and equivalent definitions.

Noetherian Schemes: Local Properties

Explains the concept of Noetherian schemes and their local properties using open sets and coverings.

The Degree of a Covering Space

Shows the equivalence between the index of a covering space's fundamental group and the degree of the covering space.

Path Lifting: Unique Path Lifting

Covers the concept of path lifting and unique path lifting property.

Quotient by Galois Action

Explores quotient by Galois action, focusing on coatings, actions, and shares in various spaces.

Universal Covering: Basics

Covers the concept of universal covering and its properties, including examples and monodromy action.

Group Theory: Restriction Functor

Explores the restriction functor in group theory, focusing on its properties.

Discrete Optimization: Set Covering

Explores the set covering problem through the example of completing a sticker collection at a minimum cost.

Lie Theorems and Group Algebra

Covers Lie theorems, group algebra, Ado's theorem, and spacetime symmetries.