Representation of -knots.
-knots via the mapping class group of the twice punctured torus.
Seifert manifolds and (1,1)-knots.
Torus knots and Dunwoody manifolds.
Generalizad Lins-Mandel Spaces and branched coverings of S.
Representations of (1,1)-knots
We present two different representations of (1,1)-knots and study some connections between them. The first representation is algebraic: every (1,1)-knot is represented by an element of the pure mapping class group of the twice punctured torus PMCG₂(T). Moreover, there is a surjective map from the kernel of the natural homomorphism Ω:PMCG₂(T) → MCG(T) ≅ SL(2,ℤ), which is a free group of rank two, to the class of all (1,1)-knots in a fixed lens space. The second representation is parametric: every...
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