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Realization of primitive branched coverings over closed surfaces following the hurwitz approach

Semeon Bogatyi, Daciberg Gonçalves, Elena Kudryavtseva, Heiner Zieschang (2003)

Open Mathematics

Let V be a closed surface, H⊑π1(V) a subgroup of finite index l and D=[A 1,...,A m] a collection of partitions of a given number d≥2 with positive defect v(D). When does there exist a connected branched covering f:W→V of order d with branch data D and f∶W→V It has been shown by geometric arguments [4] that, for l=1 and a surface V different from the sphere and the projective plane, the corresponding branched covering exists (the data D is realizable) if and only if the data D fulfills the Hurwitz...

Representation of $(1, 1)$ -knots.

Mulazzani, Michele (2006)

Sibirskie Ehlektronnye Matematicheskie Izvestiya [electronic only]

Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold

Masahito Toda (2004)

Open Mathematics

The paper studies the first homology of finite regular branched coverings of a universal Borromean orbifold called B 4,4,4ℍ3. We investigate the irreducible components of the first homology as a representation space of the finite covering transformation group G. This gives information on the first betti number of finite coverings of general 3-manifolds by the universality of B 4,4,4. The main result of the paper is a criterion in terms of the irreducible character whether a given irreducible representation...

Representations of (1,1)-knots

Alessia Cattabriga, Michele Mulazzani (2005)

Fundamenta Mathematicae

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...

Representing 3-manifolds by triangulations of $S^{3}$ . I: A constructive approach.

Hilden, Mike, Montesinos, José M., Tejada, Débora, Toro, Margarita (2005)

Revista Colombiana de Matemáticas

Representing open 3-manifolds as 3-fold branched coverings.

José María Montesinos-Amilibia (2002)

Revista Matemática Complutense

It is proved that the Freudenthal compactification of an open, connected, oriented 3-manifold is a 3-fold branched covering of S3, and in some cases, a 2-fold branched covering of S3. The branching set is a locally finite disjoint union of strings.