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Sfb 288 Differential Geometry and Quantum Physics |
Abstract for Sfb Preprint No. 386
Representation of finite groups and the first Betti number of branched coverings of a universal borromean orbifold Masahito Toda
The paper investigate the first homology of the regular branched coverings of universal Borromean orbifold $B_{1,1,1} {Bbb H}^3$, whose arithmetic structures are intensively studied in [HLM1]. The action of the group $G$ of the covering transformations on the first homology is studied to obtain a criterion for an irreducible representation of $G$ to be an irreducible component of the first homology with particular enthusiasm on the principal congruent subgroups. The investigation is motivated by a problem of the three dimensional topology due to Thurston and provides a criterion for a class of 3-manifolds to have a finite sheeted covering of positive first Betti number in terms of the group theory.
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