A note on a 3-dimensional homogeneous space

J. H. Rubinstein; C. Gardiner

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

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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...