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Lecture
Universal Covering
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Related lectures (32)
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
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.
Lifting Criterion
Explores the lifting criterion for maps between path-connected and locally path-connected spaces.
Topology: Homotopy and Cone Attachments
Discusses homotopy and cone attachments in topology, emphasizing their significance in understanding connected components and fundamental groups.
Topology: Fundamental Groups and Surfaces
Discusses fundamental groups, surfaces, and their topological properties in detail.
Topology: Fundamental Groups and Applications
Provides an overview of fundamental groups in topology and their applications, focusing on the Seifert-van Kampen theorem and its implications for computing fundamental groups.
Induced Homomorphisms on Relative Homology Groups
Covers induced homomorphisms on relative homology groups and their properties.
Homotopy Theory: Cylinders and Path Objects
Covers cylinders, path objects, and homotopy in model categories.
Group Actions and Fundamental Groups
Delves into group actions, coverings, fundamental groups, and homomorphisms in topological spaces.
Homotopy: Fundamentals and Examples
Covers the fundamentals of homotopy and its applications in topology.
Topology: Homotopy and Projective Spaces
Discusses homotopy, projective spaces, and the universal property of quotient spaces in topology.
Path Lifting
Explores path lifting, homotopy properties, and homomorphisms in covering spaces.
Homology of Riemann Surfaces
Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.
Homotopy Extension Property
Introduces the homotopy extension property, exploring conditions for extending continuous maps.
Knot Theory: The Quadratic Linking Degree
Covers the quadratic linking degree in knot theory, exploring its definitions, properties, and significance in algebraic geometry.
Contracting Subspaces
Explores the homotopy extension property for contractable subspaces and their quotient maps.
Homotopy Invariance
Explores homotopy invariance, emphasizing the preservation of properties under continuous functions and their relationship with topological spaces.
Homotopies & Equivalence Relations
Covers homotopies, fundamental group, and equivalence relations in applications.
The Topological Künneth Theorem
Explores the topological Künneth Theorem, emphasizing commutativity and homotopy equivalence in chain complexes.
Homotopical Algebra: Introduction
Introduces the course on homotopical algebra, exploring the power of analogy in pure mathematics.
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