John Berge constructed these knots as a way of creating knots with lens space Berge conjecture.
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These differed from the eyes of most trilobites in having comparatively few lenses spaced between deep sclera.
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The same holds for lens spaces ( as proved by Francis Bonahon and J . P . Otal ).
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Their example are two three-dimensional lens spaces, and the configuration spaces of at least two points in them.
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The manifolds S ^ 3 / \ Gamma with & Gamma; cyclic are precisely the 3-dimensional lens spaces.
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This is the image of the Clifford torus in S ^ 3 under the quotient map used to define the lens space in question.
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It follows from the structure of the mapping class group of the two-torus that only lens spaces have splittings of genus one.
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Reidemeister torsion was first used to combinatorially classify 3-dimensional lens spaces in by Reidemeister, and in higher-dimensional spaces by Franz.
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For instance, the Lens space L ( 4, 1 ) contains an incompressible Klein bottle that is not \ pi _ 1-injective.
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