Concept
Contractible space
Related lectures (30)
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Explores the homology of Riemann surfaces, including singular homology and the standard n-simplex.
Singular Homology: First Properties
Covers the first properties of singular homology and the preservation of decomposition and path-connected components in topological spaces.
Theory: Adjunctions
Explores the theory of adjunctions, covering their definition, properties, and applications through examples and exercises.
Homotopy Type Theory
Covers homotopy type theory, including equivalences, contractible spaces, pushouts, and applications.
Differential Forms on Manifolds
Introduces differential forms on manifolds, covering tangent bundles and intersection pairings.
Cohomology: Cross Product
Explores cohomology and the cross product, demonstrating its application in group actions like conjugation.
Fundamental Groups
Explores fundamental groups, homotopy classes, and coverings in connected manifolds.
Small Scale Stability: Equilibrium Point
Discusses stability analysis of equilibrium points in dynamical systems.
Contracting Subspaces
Explores the homotopy extension property for contractable subspaces and their quotient maps.
Universal Covering
Explores the concept of a universal cover of a topological space and the necessary conditions for a space to have one.