van Kampen theorem
E1274906
UNEXPLORED
The van Kampen theorem is a fundamental result in algebraic topology that computes the fundamental group of a space from the fundamental groups of overlapping subspaces and their intersections.
All labels observed (2)
| Label | Occurrences |
|---|---|
| van Kampen theorem canonical | 1 |
| van Kampen theorem in algebraic topology | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T17549872 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: van Kampen theorem Context triple: [Wirtinger presentation of knot groups, relatedTo, van Kampen theorem]
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A.
van Kampen diagram
A van Kampen diagram is a planar, combinatorial 2-complex used in combinatorial group theory to visually represent relations in a group presentation and to prove that a word equals the identity.
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B.
Eilenberg–MacLane spaces
Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
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C.
Hurewicz homomorphism
The Hurewicz homomorphism is a fundamental map in algebraic topology that relates the homotopy groups of a space to its homology groups, often serving as a bridge between geometric and algebraic invariants.
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D.
Künneth formula
The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
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E.
Foundations of Algebraic Topology
Foundations of Algebraic Topology is a classic graduate-level textbook by Norman Steenrod that systematically develops the fundamental concepts and tools of algebraic topology.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: van Kampen theorem Target entity description: The van Kampen theorem is a fundamental result in algebraic topology that computes the fundamental group of a space from the fundamental groups of overlapping subspaces and their intersections.
-
A.
van Kampen diagram
A van Kampen diagram is a planar, combinatorial 2-complex used in combinatorial group theory to visually represent relations in a group presentation and to prove that a word equals the identity.
-
B.
Eilenberg–MacLane spaces
Eilenberg–MacLane spaces are topological spaces characterized by having a single nontrivial homotopy group, serving as fundamental building blocks in homotopy theory and the definition of cohomology.
-
C.
Hurewicz homomorphism
The Hurewicz homomorphism is a fundamental map in algebraic topology that relates the homotopy groups of a space to its homology groups, often serving as a bridge between geometric and algebraic invariants.
-
D.
Künneth formula
The Künneth formula is a fundamental result in algebraic topology and homological algebra that expresses the (co)homology of a product space or object in terms of the (co)homology of its factors.
-
E.
Foundations of Algebraic Topology
Foundations of Algebraic Topology is a classic graduate-level textbook by Norman Steenrod that systematically develops the fundamental concepts and tools of algebraic topology.
- F. None of above. chosen
Referenced by (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
linked to: van Kampen theorem