Seiberg–Witten invariants
E861521
Seiberg–Witten invariants are powerful topological invariants of smooth four-manifolds derived from solutions to the Seiberg–Witten equations, used to distinguish different smooth structures and study the geometry and topology of 4D spaces.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Seiberg–Witten invariants canonical | 4 |
How this entity was disambiguated
This entity first appeared as the object of triple T10388677 — 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: Seiberg–Witten invariants Context triple: [Seiberg–Witten theory, relatedTo, Seiberg–Witten invariants]
-
A.
Seiberg–Witten theory
Seiberg–Witten theory is a framework in quantum field theory and string theory that uses supersymmetry to exactly analyze strongly coupled gauge theories, leading to profound insights into dualities and four-dimensional topology.
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B.
Donaldson invariants
Donaldson invariants are sophisticated topological invariants of smooth four-dimensional manifolds derived from moduli spaces of anti-self-dual connections, central to the study of 4-manifold differential topology.
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C.
Seiberg–Witten differential
The Seiberg–Witten differential is a meromorphic one-form on the Seiberg–Witten curve whose periods encode the low-energy effective couplings and BPS spectrum of certain supersymmetric gauge theories.
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D.
Seiberg–Witten curve
The Seiberg–Witten curve is an auxiliary complex algebraic curve encoding the low-energy effective dynamics of certain supersymmetric gauge theories, particularly their moduli spaces and BPS spectra.
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E.
Donaldson–Witten theory
Donaldson–Witten theory is a four-dimensional topological quantum field theory derived from twisting N=2 supersymmetric Yang–Mills theory, used to compute Donaldson invariants of smooth four-manifolds.
- 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: Seiberg–Witten invariants Target entity description: Seiberg–Witten invariants are powerful topological invariants of smooth four-manifolds derived from solutions to the Seiberg–Witten equations, used to distinguish different smooth structures and study the geometry and topology of 4D spaces.
-
A.
Seiberg–Witten theory
Seiberg–Witten theory is a framework in quantum field theory and string theory that uses supersymmetry to exactly analyze strongly coupled gauge theories, leading to profound insights into dualities and four-dimensional topology.
-
B.
Donaldson invariants
Donaldson invariants are sophisticated topological invariants of smooth four-dimensional manifolds derived from moduli spaces of anti-self-dual connections, central to the study of 4-manifold differential topology.
-
C.
Seiberg–Witten differential
The Seiberg–Witten differential is a meromorphic one-form on the Seiberg–Witten curve whose periods encode the low-energy effective couplings and BPS spectrum of certain supersymmetric gauge theories.
-
D.
Seiberg–Witten curve
The Seiberg–Witten curve is an auxiliary complex algebraic curve encoding the low-energy effective dynamics of certain supersymmetric gauge theories, particularly their moduli spaces and BPS spectra.
-
E.
Donaldson–Witten theory
Donaldson–Witten theory is a four-dimensional topological quantum field theory derived from twisting N=2 supersymmetric Yang–Mills theory, used to compute Donaldson invariants of smooth four-manifolds.
- F. None of above. chosen
Statements (48)
| Predicate | Object |
|---|---|
| instanceOf |
gauge-theoretic invariant
ⓘ
smooth 4-manifold invariant ⓘ topological invariant ⓘ |
| constructedFrom |
count of solutions to Seiberg–Witten equations
ⓘ
oriented moduli space of solutions ⓘ |
| definedOn |
oriented smooth 4-manifolds
ⓘ
smooth four-manifolds ⓘ |
| definedUsing |
Seiberg–Witten equations
ⓘ
moduli space of monopoles ⓘ solutions of Seiberg–Witten equations ⓘ spin^c structures ⓘ |
| dependsOn |
chamber structure in b2^+ = 1 case
ⓘ
choice of spin^c structure ⓘ |
| field |
4-manifold topology
ⓘ
differential topology ⓘ gauge theory ⓘ geometric analysis ⓘ symplectic topology ⓘ |
| generalizes | earlier gauge-theoretic invariants of 4-manifolds ⓘ |
| hasVariant |
equivariant Seiberg–Witten invariants
ⓘ
monopole Floer homology ⓘ relative Seiberg–Witten invariants ⓘ |
| implies | adjunction inequality for embedded surfaces ⓘ |
| inspiredBy |
quantum field theory
ⓘ
supersymmetric gauge theory ⓘ |
| introducedBy |
Edward Witten
ⓘ
Nathan Seiberg ⓘ |
| relatedTo |
Donaldson invariants
ⓘ
Floer homology ⓘ
linked to:
Floer theory
Heegaard Floer homology ⓘ
linked to:
Floer theory
Yang–Mills gauge theory ⓘ
linked to:
Yang–Mills theory
monopole equations ⓘ |
| requires |
compactness of moduli space
ⓘ
transversality of moduli space ⓘ |
| sensitiveTo | smooth structure but not just homeomorphism type ⓘ |
| simplifiedComputationComparedTo | Donaldson invariants ⓘ |
| takesValuesIn | integers ⓘ |
| usedFor |
detecting exotic smooth structures
ⓘ
distinguishing homeomorphic but non-diffeomorphic 4-manifolds ⓘ distinguishing smooth structures on 4-manifolds ⓘ proving non-existence of metrics of positive scalar curvature ⓘ studying geometry of 4-manifolds ⓘ studying symplectic structures on 4-manifolds ⓘ studying topology of 4-manifolds ⓘ |
| usedToProve |
Thom conjecture for CP^2
ⓘ
constraints on intersection forms of 4-manifolds ⓘ |
| wellDefinedWhen | b2^+ > 1 ⓘ |
| yearIntroduced | 1994 ⓘ |
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Subject: Seiberg–Witten invariants Description of subject: Seiberg–Witten invariants are powerful topological invariants of smooth four-manifolds derived from solutions to the Seiberg–Witten equations, used to distinguish different smooth structures and study the geometry and topology of 4D spaces.
Referenced by (4)
Full triples — surface form annotated when it differs from this entity's canonical label.