The set of all versors, or unit quaternions, forms this type of manifold.
A foliation of this object is named for Reeb, while a fibration describing this object is known as the Hopf bundle. This object is homeomorphic to the one-point compactification of the 3-dimensional Euclidean space. The set of all versors, or unit quaternions, forms this type of manifold. As a Lie group, this object is equivalent to the symplectic group Sp(1) and diffeomorphic to SU(2), which implies that it is parallelizable. A 2002 e-print on the arXiv ("archive") titled "The entropy formula for the (*) Ricci flow and its geometric applications" was the first of a series of three posts resolving a major question about these objects. Any simply connected closed 3-manifold is homeomorphic to this object, as was proven by Grigori Perelman in the Poincaré conjecture. For 10 points, name this object which can be thought of as the boundary of a 4-dimensional ball, a higher-dimensional analogue of a sphere.
A foliation of this object is named for Reeb, while a fibration describing this object is known as the Hopf bundle.
3-sphere [prompt on "sphere" or "hypersphere"; accept S3; apparently you can accept glome]