Concept

Covering space

Related lectures (31)

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.

Bar Construction: Homology Groups and Classifying Space

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

Universal Covering

Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.

Holomorphic Functions: Taylor Series Expansion

Covers the basic properties of holomorphic maps and Taylor series expansions in complex analysis.

Universal Covering Construction

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

Group Actions and Fundamental Groups

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

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: Basics

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

Open Mapping Theorem

Explains the Open Mapping Theorem for holomorphic maps between Riemann surfaces.

Lifting Criterion

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

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.

Path Lifting: Unique Path Lifting

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

Path Lifting

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

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.

Quotient by Galois Action

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

Electromagnetic Problems: Well-Posedness and Convergence

Explores the well-posedness and convergence of electromagnetic problems, including continuity interpolation, Darcy's law, and surjectivity properties.

Discrete Optimization: Set Covering

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

Adjunctions and Push Outs

Covers adjunctions, push outs, colimits, and discrete fibers in coverings, emphasizing group actions and symmetries.