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Concept

Covering space

Related lectures (31)

Fundamental Groups

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

Local Homeomorphisms and Coverings

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.

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.

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.

Quotient by Galois Action

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

Discrete Optimization: Set Covering MOOC: Optimization: principles and algorithms - Network and discrete optimization

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.

Isomorphism in Aut(p)

Explores isomorphism between Aut(p) and a Galois covering through topology course notes.

Topology: Classification of Surfaces and Fundamental Groups

Discusses the classification of surfaces and their fundamental groups using the Seifert-van Kampen theorem and polygonal presentations.

Open Subsets and Compact Sets

Discusses open subsets, compact sets, and methods for demonstrating openness in a space.

Quantum Mechanics Rotations

Delves into quantum mechanical rotations, discussing SU(2), SO(3), group representations, and topological properties.

Connected Components

Explores connected components in a decked space and the well-defined application of functions.

Understanding Vibrations

Explores vibrations, their properties, and how any map can be transformed into a vibration through factorization.