|
gptkbp:instanceOf
|
gptkb:mathematical_concept
gptkb:topology
gptkb:Riemannian_manifold
|
|
gptkbp:appearsIn
|
gptkb:Poincaré_conjecture
|
|
gptkbp:borders
|
none
|
|
gptkbp:can_be_parameterized_by
|
hyperspherical coordinates
|
|
gptkbp:can_be_visualized_as
|
set of unit quaternions
|
|
gptkbp:describes
|
set of points in R^4 at unit distance from origin
unit sphere in 4 dimensions
|
|
gptkbp:dimensions
|
3
|
|
gptkbp:embedded_in
|
gptkb:4-dimensional_Euclidean_space
|
|
gptkbp:Euler_characteristic
|
0
|
|
gptkbp:fiber_in_Hopf_fibration
|
gptkb:circle_(S^1)
|
|
gptkbp:first_Chern_class
|
0
|
|
gptkbp:fundamentalGroup
|
trivial
|
|
gptkbp:generalizes
|
gptkb:butter
|
|
gptkbp:hasModel
|
gptkb:3-dimensional_spherical_geometry
|
|
gptkbp:hasSpecialCase
|
n-sphere
|
|
gptkbp:homeomorphic_to
|
unit quaternions
|
|
gptkbp:homology_group_H_0
|
Z
|
|
gptkbp:homology_group_H_1
|
0
|
|
gptkbp:homology_group_H_2
|
0
|
|
gptkbp:homology_group_H_3
|
Z
|
|
https://www.w3.org/2000/01/rdf-schema#label
|
3-sphere
|
|
gptkbp:is_a_closed_manifold
|
yes
|
|
gptkbp:is_a_compact_manifold
|
yes
|
|
gptkbp:is_a_covering_space_of
|
3-dimensional real projective space
|
|
gptkbp:is_a_double_cover_of
|
gptkb:SO(3)
|
|
gptkbp:is_a_fiber_bundle_over
|
2-sphere
|
|
gptkbp:is_a_homogeneous_space
|
yes
|
|
gptkbp:is_a_parallelizable_manifold
|
yes
|
|
gptkbp:is_a_Riemannian_manifold
|
yes
|
|
gptkbp:is_a_smooth_manifold
|
yes
|
|
gptkbp:is_a_solution_to
|
gptkb:Poincaré_conjecture
|
|
gptkbp:orientable
|
yes
|
|
gptkbp:relatedTo
|
gptkb:SU(2)
gptkb:Hopf_fibration
quaternions
orthogonal group
|
|
gptkbp:simply_connected
|
yes
|
|
gptkbp:structure
|
gptkb:SU(2)
gptkb:Lie_group
|
|
gptkbp:symbol
|
S^3
|
|
gptkbp:used_in
|
gptkb:cosmology
gptkb:geometry
gptkb:theoretical_physics
gptkb:topology
|
|
gptkbp:volume
|
2π^2
|
|
gptkbp:bfsParent
|
gptkb:torus_link
gptkb:Hopf_fibration
|
|
gptkbp:bfsLayer
|
5
|