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 (2)
| Label | Occurrences |
|---|---|
| Sullivan minimal model in rational homotopy theory canonical | 1 |
| minimal Sullivan algebra | 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.
-
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 ⓘ |
| isQuasiIsomorphicTo | piecewise linear differential forms on the space ⓘ |
| isRelatedConcept | minimal Sullivan algebra ⓘ |
| isToolFor |
classifying spaces up to rational homotopy equivalence
ⓘ
computing rational homotopy invariants ⓘ |
| isUniqueUpTo | isomorphism of commutative differential graded algebras ⓘ |
| isUsedToStudy |
Massey products
ⓘ
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
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
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 (2)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject linked to:
Sullivan minimal model in rational homotopy theory
linked to: Sullivan minimal model in rational homotopy theory