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gptkbp:instanceOf
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gptkb:algebraic_geometry
gptkb:mathematical_concept
gptkb:topology
gptkb:fiber
gptkb:Riemannian_manifold
gptkb:Lie_group
Kähler manifold
abelian group
symplectic manifold
covering space
principal bundle
homogeneous space
parallelizable manifold
product manifold
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gptkbp:compact
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true
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gptkbp:definedIn
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product of n circles
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gptkbp:dimensions
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n
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gptkbp:firstHomologyGroup
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Z^n
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gptkbp:fundamentalGroup
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Z^n
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gptkbp:hasConnection
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true
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gptkbp:hasFlatMetric
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true
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gptkbp:hasSpecialCase
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1-torus is the circle
2-torus is the torus
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gptkbp:homologyGroup
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direct sum of binomial(n,k) copies of Z in degree k
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https://www.w3.org/2000/01/rdf-schema#label
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n-torus
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gptkbp:isAbelianLieGroup
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true
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gptkbp:isAlgebraicGroup
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true
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gptkbp:isComplexManifold
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true
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gptkbp:isFiberBundleOver
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(n-1)-torus
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gptkbp:isGroupManifold
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true
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gptkbp:isHomogeneousSpace
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true
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gptkbp:isKählerManifold
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true
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gptkbp:isMatrixGroup
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true
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gptkbp:isOrientable
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true
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gptkbp:isParallelizable
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true
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gptkbp:isPrincipalBundle
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true
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gptkbp:isProductManifold
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true
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gptkbp:isQuotientOf
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gptkb:R^n_/_Z^n
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gptkbp:isSymplecticManifold
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true
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gptkbp:notation
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(S^1)^n
T^n
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gptkbp:universalCover
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R^n
itself
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gptkbp:bfsParent
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gptkb:Torus
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gptkbp:bfsLayer
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6
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