Sullivan minimal model in rational homotopy theory
E596068
The Sullivan minimal model in rational homotopy theory is a canonical commutative differential graded algebra that encodes the rational homotopy type of a topological space in an algebraic form.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Sullivan minimal model in rational homotopy theory canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T6475544 — 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: Sullivan minimal model in rational homotopy theory Context triple: [Dennis Sullivan, hasWork, Sullivan minimal model in rational homotopy theory]
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A.
L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
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B.
Grothendieck spectral sequence
The Grothendieck spectral sequence is a fundamental tool in homological algebra that relates the derived functors of a composite functor to the derived functors of its components, enabling efficient computation of cohomology.
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C.
Atiyah–Hirzebruch spectral sequence
The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
-
D.
Cartan theorems A and B
Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
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E.
Serre spectral sequence
The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
- 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: Sullivan minimal model in rational homotopy theory Target entity description: The Sullivan minimal model in rational homotopy theory is a canonical commutative differential graded algebra that encodes the rational homotopy type of a topological space in an algebraic form.
-
A.
L’Analysis Situs et la Géométrie Algébrique
L’Analysis Situs et la Géométrie Algébrique is a foundational mathematical treatise that helped establish modern algebraic topology and its connections with algebraic geometry.
-
B.
Grothendieck spectral sequence
The Grothendieck spectral sequence is a fundamental tool in homological algebra that relates the derived functors of a composite functor to the derived functors of its components, enabling efficient computation of cohomology.
-
C.
Atiyah–Hirzebruch spectral sequence
The Atiyah–Hirzebruch spectral sequence is a fundamental computational tool in algebraic topology that relates generalized cohomology theories, such as K-theory, to ordinary cohomology, enabling the step-by-step calculation of these invariants from simpler data.
-
D.
Cartan theorems A and B
Cartan theorems A and B are fundamental results in complex analytic geometry that characterize coherent analytic sheaves on Stein spaces by guaranteeing the existence of enough global sections and the vanishing of higher cohomology.
-
E.
Serre spectral sequence
The Serre spectral sequence is a fundamental tool in algebraic topology that relates the homology or cohomology of a fibration to that of its base and fiber, enabling complex computations in a systematic way.
- F. None of above. chosen
Statements (47)
| Predicate | Object |
|---|---|
| instanceOf |
commutative differential graded algebra
ⓘ
invariant in rational homotopy theory ⓘ minimal model ⓘ |
| appliesTo |
nilpotent CW-complexes of finite type
ⓘ
simply connected finite CW-complexes ⓘ |
| associatedWith |
nilpotent spaces of finite type
ⓘ
simply connected topological spaces ⓘ |
| captures |
rational Postnikov tower data
ⓘ
rational homotopy groups of a space ⓘ |
| determines | rational homotopy groups via duality ⓘ |
| encodes | rational homotopy type of a topological space ⓘ |
| field | rational homotopy theory ⓘ |
| hasBaseField | rational numbers ⓘ |
| hasCategory | category of commutative differential graded algebras over ℚ ⓘ |
| hasCohomologyIsomorphicTo | rational cohomology of the space ⓘ |
| hasDifferential | degree +1 differential ⓘ |
| hasEquivalenceClass | quasi-isomorphism class of cdgas ⓘ |
| hasGeneratorDegrees | positive integers (for simply connected spaces) ⓘ |
| hasMorphismsCorrespondingTo | rational homotopy classes of maps between spaces ⓘ |
| hasProperty |
differential decomposable on generators
ⓘ
free as a graded commutative algebra on generators ⓘ minimal ⓘ |
| hasStructure |
differential graded algebra
ⓘ
graded commutative algebra ⓘ |
| isCanonicalFor | rational homotopy type ⓘ |
| isConstructedBy | inductive extension by generators and relations ⓘ |
| isConstructedFrom | polynomial differential forms on simplices ⓘ |
| isDefinedFor | connected CW-complexes of finite type ⓘ |
| isDefinedOver | ℚ ⓘ |
| isEquivalentTo | Quillen model in rational homotopy theory (up to equivalence) ⓘ |
| isExampleOf | algebraic model of a topological space ⓘ |
| isFunctor | from homotopy category of suitable spaces to homotopy category of cdgas ⓘ |
| isFunctorialIn | topological spaces (up to homotopy) ⓘ |
| isMinimalIf | differential has no linear part on generators ⓘ |
| isNamedAfter | Dennis Sullivan NERFINISHED ⓘ |
| isQuasiIsomorphicTo | piecewise linear differential forms on the space ⓘ |
| isRelatedConcept | minimal Sullivan algebra NERFINISHED ⓘ |
| isToolFor |
classifying spaces up to rational homotopy equivalence
ⓘ
computing rational homotopy invariants ⓘ |
| isUniqueUpTo | isomorphism of commutative differential graded algebras ⓘ |
| isUsedToStudy |
Massey products
NERFINISHED
ⓘ
formality of spaces ⓘ rational LS-category ⓘ rational homotopy type of manifolds ⓘ |
| relatesTo |
de Rham algebra of differential forms
ⓘ
piecewise linear de Rham complex A_{PL}(X) ⓘ |
| usesConvention | cohomological grading ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
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Input
Subject: Sullivan minimal model in rational homotopy theory Description of subject: The Sullivan minimal model in rational homotopy theory is a canonical commutative differential graded algebra that encodes the rational homotopy type of a topological space in an algebraic form.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.