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Examples
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So I presume that the cyclic group, or homotopy on the 3-sphere persists for N-large or for classical recovery.
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By the Rokhlin theorem a region of a four dimensional space that is bounded by a homology 3-sphere is a spin manifold.
The Lopsided Universe Sean 2008
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(In the standard closed universe model the final c-boundary is a 3-sphere.)
The FAP Flop Tipler, Frank J. 1986
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Universe - the part of spacetime that is not temporal, takes a 3-sphere form - the four-dimensional counterpart to a sphere.
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He made the now-infamous three-dimensional sphere-or 3-sphere-as long as you don't tear it, puncture it, or crease, it is still, mathematically speaking, a 3-sphere.
SEEDMAGAZINE.COM boustead@seedmediagroup.com 2010
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The surprise is that electrons confined to the surface of a 3-sphere (ie to the surface of a 4-D ball) behave in a remarkably similar way to electrons confined to real 3D space.
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He made the now-infamous three-dimensional sphere-or 3-sphere-as long as you don't tear it, puncture it, or crease, it is still, mathematically speaking, a 3-sphere.
SEEDMAGAZINE.COM montenegro@seedmediagroup.com 2010
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But because the universe is a 3-sphere in Shu's models, the flatness problem "disappears automatically."
PhysOrg.com - latest science and technology news stories 2010
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• The spatial section of the universe is a 3-sphere [a higher-dimensional analogue of a sphere], ruling out the possibility of a flat or hyperboloid geometry.
PhysOrg.com - latest science and technology news stories 2010
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(they are stereographically projected onto a 3-sphere, rotated and projected back down to flat 3-space)
Why Can’t We Visualize More Than Three Dimensions? Sean 2009
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