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gptkbp:instanceOf
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gptkb:topology
gptkb:Riemannian_manifold
|
|
gptkbp:can_be_defined_as
|
set of points in R^8 at unit distance from origin
|
|
gptkbp:can_be_parallelized
|
yes
|
|
gptkbp:dimensions
|
7
|
|
gptkbp:Euler_characteristic
|
0
|
|
gptkbp:exotic_spheres_in_dimension_7
|
28
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:has_exotic_smooth_structures
|
yes
|
|
gptkbp:hasConnection
|
yes
|
|
gptkbp:homology_group_H_0(S^7)
|
Z
|
|
gptkbp:homology_group_H_7(S^7)
|
Z
|
|
gptkbp:homology_group_H_k(S^7)
|
0 for 0<k<7
|
|
gptkbp:homotopy_group_π_7(S^7)
|
Z
|
|
gptkbp:Hopf_fibration
|
S^3 → S^7 → S^4
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
7-sphere (S^7)
|
|
gptkbp:is_a_boundary
|
no
|
|
gptkbp:is_a_boundaryless_manifold
|
yes
|
|
gptkbp:is_a_closed_manifold
|
yes
|
|
gptkbp:is_a_closed_smooth_manifold
|
yes
|
|
gptkbp:is_a_compact_connected_manifold
|
yes
|
|
gptkbp:is_a_compact_manifold
|
yes
|
|
gptkbp:is_a_compact_metric_space
|
yes
|
|
gptkbp:is_a_compact_orientable_manifold
|
yes
|
|
gptkbp:is_a_compact_Riemannian_manifold
|
yes
|
|
gptkbp:is_a_compact_smooth_manifold
|
yes
|
|
gptkbp:is_a_compact_space
|
yes
|
|
gptkbp:is_a_compact_topological_space
|
yes
|
|
gptkbp:is_a_connected_space
|
yes
|
|
gptkbp:is_a_hypersphere
|
yes
|
|
gptkbp:is_a_Lie_group
|
no
|
|
gptkbp:is_a_metric_space
|
yes
|
|
gptkbp:is_a_Riemannian_manifold
|
yes
|
|
gptkbp:is_a_simply_connected_space
|
yes
|
|
gptkbp:is_a_smooth_manifold
|
yes
|
|
gptkbp:is_a_smooth_sphere
|
yes
|
|
gptkbp:is_a_smoothable_topological_manifold
|
yes
|
|
gptkbp:is_a_sphere
|
yes
|
|
gptkbp:is_a_topological_sphere
|
yes
|
|
gptkbp:is_orientable
|
yes
|
|
gptkbp:is_parallelizable
|
yes
|
|
gptkbp:notation
|
S^7
|
|
gptkbp:related_to_Hopf_fibration
|
yes
|
|
gptkbp:relatedTo
|
gptkb:octonions
|
|
gptkbp:volume_(unit_sphere)
|
π^4/3
|
|
gptkbp:bfsParent
|
gptkb:SO(8)
|
|
gptkbp:bfsLayer
|
7
|