n-torus

URI: https://gptkb.org/entity/n-torus

GPTKB entity

Predicate	Object
gptkbp:instanceOf	gptkb:algebraic_geometry gptkb:mathematical_concept gptkb:topology gptkb:abelian_group gptkb:symplectic_manifold gptkb:homogeneous_space gptkb:fiber gptkb:Riemannian_manifold gptkb:parallelizable_manifold gptkb:Lie_group gptkb:Kähler_manifold gptkb:product_manifold gptkb:covering_space gptkb:principal_bundle
gptkbp:compact	true
gptkbp:definedIn	product of n circles
gptkbp:dimensions	n
gptkbp:firstHomologyGroup	Z^n
gptkbp:fundamentalGroup	Z^n
gptkbp:hasConnection	true
gptkbp:hasFlatMetric	true
gptkbp:hasSpecialCase	1-torus is the circle 2-torus is the torus
gptkbp:homologyGroup	direct sum of binomial(n,k) copies of Z in degree k
gptkbp:isAbelianLieGroup	true
gptkbp:isAlgebraicGroup	true
gptkbp:isComplexManifold	true
gptkbp:isFiberBundleOver	(n-1)-torus
gptkbp:isGroupManifold	true
gptkbp:isHomogeneousSpace	true
gptkbp:isKählerManifold	true
gptkbp:isMatrixGroup	true
gptkbp:isOrientable	true
gptkbp:isParallelizable	true
gptkbp:isPrincipalBundle	true
gptkbp:isProductManifold	true
gptkbp:isQuotientOf	gptkb:R^n_/_Z^n
gptkbp:isSymplecticManifold	true
gptkbp:notation	(S^1)^n T^n
gptkbp:universalCover	R^n itself
gptkbp:bfsParent	gptkb:Torus
gptkbp:bfsLayer	7
https://www.w3.org/2000/01/rdf-schema#label	n-torus