Lens space

Common card · No. 464453

A lens space is an example of a topological space, considered in mathematics. The term often refers to a specific class of 3-manifolds, but in general can be defined for higher dimensions. In the 3-manifold case, a lens space can be visualized as the result of gluing two solid tori together by a homeomorphism of their boundaries. Often the 3-sphere and S 2 × S 1 {\displaystyle S^{2}\times S^{1}} , both of which can be obtained as above, are not counted as they are considered trivial special cases. The three-dimensional lens spaces L ( p ; q ) {\displaystyle L(p;q)} were introduced by Heinrich Tietze in 1908. They were the first known examples of 3-manifolds which were not determined by their homology and fundamental group alone, and the simplest...

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