Wyniki wyszukiwania

Sortuj według:

Ogranicz wyniki do:

Representations of (1,1)-knots

100%

Cattabriga A., Mulazzani M.

Fundamenta Mathematicae

2005

tom 188

nr 1

45-57

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 (1,1)-knot can be represented by a 4-tuple (a,b,c,r) of integer parameters such that a,b,c ≥ 0 and $r ∈ ℤ_{2a+b+c}$. The strict connection of this representation with the class of Dunwoody manifolds is illustrated. The above representations are explicitly obtained in some interesting cases, including two-bridge knots and torus knots.

Ograniczanie wyników

1 Fundamenta Mathematicae

1 Cattabriga A.

1 Mulazzani M.

1 2005

Wyniki wyszukiwania

Representations of (1,1)-knots