overview of algebraic topology
Algebraic topology (AT) utilizes algebraic
approaches to solve topological
problems, such as the classification
of surfaces, proving duality
theorems
for manifolds and approximation theorems for topological spaces. A central problem in algebraic topology is to find algebraic invariants of topological spaces, which is usually carried out by means
of homotopy, homology and cohomology groups. There are close connections between algebraic topology,
Algebraic Geometry (AG)
- homotopy theory
and fundamental groups
- Topology and groupoids; van Kampen theorem
- Homology and cohomology theories
- Duality
- category theory applications
in algebraic topology
- indexes of category, functors
and natural transformations
- Grothendieck's Descent theory
- `Anabelian geometry'
- Categorical Galois theory
- higher dimensional algebra
(HDA)
- Quantum algebraic topology (QAT)
- Non-Abelian Quantum Algebraic Topology
(
)
- Quantum Geometry
- Non-Abelian algebraic topology (NAAT)
- Homotopy
- Fundamental group of a space
- Fundamental theorems
- van Kampen theorem
- Whitehead groups, torsion and towers
- Postnikov towers
- Topology definition, axioms and basic concepts
- fundamental groupoid
- topological groupoid
- van Kampen theorem for groupoids
- Groupoid pushout theorem
- double groupoids
and crossed modules
- new4
- homology group
- Homology sequence
- Homology complex
- new4
- Cohomology group
- Cohomology sequence
- DeRham cohomology
- new4
- crossed complexes
- modules
- omega-groupoids
- double groupoids
- Higher Homotopy van Kampen Theorems
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As of this snapshot date, this entry was owned by bci1.