Algebraic Topology
Explore paths and coverings; homology; cohomology and applications. Concepts and connections are available independently of video coverage.
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Homotopy
A homotopy continuously deforms one map into another.
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Fundamental group
Based loops modulo endpoint-fixed homotopy form a group under concatenation.
Homotopy equivalence
Maps with inverse compositions homotopic to identities describe spaces with the same homotopy type.
Simplicial complexes
Simplices fitted together along faces provide combinatorial models of spaces.
Topological manifolds
A manifold locally resembles Euclidean space with suitable separation and countability conditions.
Topological spaces
A topology specifies open sets closed under arbitrary unions and finite intersections.
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- Topological manifolds · Related · Map context
- Fundamental group · Related · Map context
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- Fundamental group · Related · Map context
- Homotopy equivalence · Related · Map context
- Topological spaces · Related · Map context
- Simplicial complexes · Related · Map context
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Topology
Explore spaces and continuity; global properties and constructions; separation and invariants. Concepts and connections are available independently of video coverage.