Representation of finite groups and the first Betti number of branched coverings of a universal Borromean orbifold (Q1767460)

The author studies the first homology of finite regular branched coverings of a universal Borromean orbifold. The main result of the paper gives a criterion for when an irreducible representation of a finite covering transformation group \(G\) is an irreducible component of the first homology if \(G\) has certain symmetries. This provides also information on the first Betti number of finite coverings of general 3-manifolds. The investigation is motivated by a problem (raised by Thurston) in 3-dimensional topology, namely, does any 3-manifold with infinite fundamental group have a finite-sheeted cover with positive first Betti number?