Donaldson invariants

E508544

4-manifold invariant gauge-theoretic invariant smooth structure invariant topological invariant

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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All labels observed (1)

Label	Occurrences
Donaldson invariants canonical	2

Statements (54)

Predicate	Object
instanceOf	4-manifold invariant ⓘ gauge-theoretic invariant ⓘ smooth structure invariant ⓘ topological invariant ⓘ
constructedFrom	cohomology classes on moduli space of anti-self-dual connections ⓘ evaluation of cohomology classes on fundamental class of moduli space ⓘ
definedOn	simply connected 4-manifold ⓘ smooth closed oriented 4-manifold ⓘ
dependsOn	smooth structure of the 4-manifold ⓘ
domain	second homology of the 4-manifold ⓘ
field	4-manifold theory ⓘ differential topology ⓘ gauge theory ⓘ geometric topology ⓘ
generalizationOf	intersection form invariants ⓘ
hasVariant	Donaldson polynomial NERFINISHED ⓘ Donaldson series NERFINISHED ⓘ polynomial Donaldson invariants ⓘ
implies	intersection form of a smooth simply connected definite 4-manifold is diagonalizable over the integers ⓘ
independentOf	Riemannian metric up to deformation ⓘ choice of generic perturbations ⓘ
inspired	applications of gauge theory to low-dimensional topology ⓘ development of Seiberg–Witten theory ⓘ
introducedBy	Simon Donaldson NERFINISHED ⓘ
namedAfter	Simon Donaldson NERFINISHED ⓘ
relatedTo	Floer homology NERFINISHED ⓘ Seiberg–Witten invariants ⓘ Witten’s topological quantum field theory NERFINISHED ⓘ instanton Floer homology ⓘ
requires	compactification of moduli space via ideal instantons ⓘ generic metric on the 4-manifold ⓘ transversality for moduli space ⓘ
takesValuesIn	cohomology ring of the moduli space ⓘ polynomial ring over the rationals ⓘ
usedTo	constrain intersection forms of smooth 4-manifolds ⓘ detect exotic smooth structures on 4-manifolds ⓘ distinguish homeomorphic but non-diffeomorphic 4-manifolds ⓘ
usesConcept	Fredholm operator ⓘ SU(2) connections ⓘ Uhlenbeck compactness NERFINISHED ⓘ Yang–Mills theory NERFINISHED ⓘ anti-self-dual connection ⓘ cohomology ⓘ compactification of moduli space ⓘ elliptic partial differential equation ⓘ homology ⓘ index theory ⓘ instanton ⓘ intersection form ⓘ moduli space of anti-self-dual connections ⓘ orientation of moduli space ⓘ principal G-bundle ⓘ smooth four-dimensional manifold ⓘ
yearIntroducedApprox	1980s ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

topological quantum field theory → producesInvariant → Donaldson invariants ⓘ

Simon Donaldson → knownFor → Donaldson invariants ⓘ