Coloured Knots and Permu- Tations Representing 3-mani- Folds
نویسنده
چکیده
It is known that every closed orientable 3-manifold can be represented by coloured knots ((4], 5]), edge-coloured graphs ((2]) or transitive permutation pairs ((6]). The present paper describes some relations between these representation theories: in particular, it is shown how to obtain a transitive permutation pair representing a 3-manifold M 3 , starting from a coloured knot representing M 3 .
منابع مشابه
Loopless Generation of Multiset Permutations by Prefix Shifts
This paper answers the following mathematical question: Can multiset permu-tations be ordered so that each permutation is a prefix shift of the previous permutation?Previously, the answer was known for the permutations of any set, and the permutationsof any multiset whose corresponding set contains only two elements. This paper also an-swers the following algorithmic question: C...
متن کاملSurgery Presentations of Coloured Knots and of Their Covering Links
We consider knots equipped with a representation of their knot groups onto a dihedral group D2n (where n is odd). To each such knot there corresponds a closed 3–manifold, the (irregular) dihedral branched covering space, with the branching set over the knot forming a link in it. We report a variety of results relating to the problem of passing from the initial data of a D2n-coloured knot to a s...
متن کاملColoured Untying of Knots
For p 3 and for p 5 we show that every p-coloured knot K can be reduced to a left-hand pp, 2q-torus knot by a sequence of surgeries along components in the kernel of its p-colouring ρ : π1pS3 Kq ÝÑ D2p . This gives us a 3-colour and a 5-colour analogue of the surgery presentation of a knot in the complement of an unknot. AMS Classification 57M25; 57M10,57M27
متن کاملJu n 20 01 The many faces of cyclic branched coverings of 2 - bridge knots and links ∗
We discuss 3-manifolds which are cyclic coverings of the 3-sphere, branched over 2-bridge knots and links. Different descriptions of these manifolds are presented: polyhedral, Heegaard diagram, Dehn surgery and coloured graph constructions. Using these descriptions, we give presentations for their fundamental groups, which are cyclic presentations in the case of 2-bridge knots. The homology gro...
متن کاملA Note on Rigidity of 3-Sasakian Manifolds
Making use of the relations among 3-Sasakian manifolds, hypercomplex mani-folds and quaternionic KK ahler orbifolds, we prove that complete 3-Sasakian manifolds are rigid.
متن کامل