John Berge constructed these knots as a way of creating knots with lens space Berge conjecture.
3.
These differed from the eyes of most trilobites in having comparatively few lenses spaced between deep sclera.
4.
The same holds for lens spaces ( as proved by Francis Bonahon and J . P . Otal ).
5.
Their example are two three-dimensional lens spaces, and the configuration spaces of at least two points in them.
6.
The manifolds S ^ 3 / \ Gamma with & Gamma; cyclic are precisely the 3-dimensional lens spaces.
7.
This is the image of the Clifford torus in S ^ 3 under the quotient map used to define the lens space in question.
8.
It follows from the structure of the mapping class group of the two-torus that only lens spaces have splittings of genus one.
9.
Reidemeister torsion was first used to combinatorially classify 3-dimensional lens spaces in by Reidemeister, and in higher-dimensional spaces by Franz.
10.
For instance, the Lens space L ( 4, 1 ) contains an incompressible Klein bottle that is not \ pi _ 1-injective.
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