Double suspension theorem
Encyclopedia
In geometric topology
, the double suspension theorem of and R. D. Edwards states that the double suspension S2X of a homology sphere
X is a topological sphere.
The double suspension of a piecewise-linear homology sphere that is not a sphere is an example of triangulation of a topological sphere that is not piecewise-linear, because the link of a point is not a sphere.
Geometric topology
In mathematics, geometric topology is the study of manifolds and maps between them, particularly embeddings of one manifold into another.- Topics :...
, the double suspension theorem of and R. D. Edwards states that the double suspension S2X of a homology sphere
Homology sphere
In algebraic topology, a homology sphere is an n-manifold X having the homology groups of an n-sphere, for some integer n ≥ 1. That is,andTherefore X is a connected space, with one non-zero higher Betti number: bn...
X is a topological sphere.
The double suspension of a piecewise-linear homology sphere that is not a sphere is an example of triangulation of a topological sphere that is not piecewise-linear, because the link of a point is not a sphere.