It is well-known that every closed orientable 3-manifold M 3 is the 3-fold simple covering M3(K,o)) of S 3 branched over a knot K: hence, M 3 may be visualized by the associated coloured knot (K, co). On the other hand, PL-manifolds of arbitrary dimension may be represented by coloured graphs, via p
Representing branched coverings by Edge-Coloured Graphs
β Scribed by Maria Rita Casali; Luigi Grasselli
- Publisher
- Elsevier Science
- Year
- 1989
- Tongue
- English
- Weight
- 539 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0166-8641
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β¦ Synopsis
Given a link L ~ S 3, we describe a standard method for constructing a class l~, d of 4-coloured graphs representing all closed orientable 3-manifolds which are d-fold coverings of S 3 branched over the link L.
π SIMILAR VOLUMES
We prove that every connected graph on n vertices can be covered by at most nΓ2+O(n 3Γ4 ) paths. This implies that a weak version of a well-known conjecture of Gallai is asymptotically true.
In this paper it is proved that the exponential generating function of the numbers, denoted by N(p, q), of irreducible coverings by edges of the vertices of complete bipartite graphs Kp.q equals exp(xe r + ye x -x -y -xy) -t.