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

• Autorzy: Masahito Toda
• Języki publikacji: EN

Abstrakty

EN

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 of G is an irreducible component of the first homology when G admits certain symmetries. As a special case of the motivating argument the criterion is applied to principal congruence subgroups of B 4,4,4. The group theoretic computation shows that most of the, possibly nonprincipal, congruence subgroups are of positive first Betti number.

Słowa kluczowe

EN

hyperbolic geometry; 3-manifold; arithmetic lattice; finite groups of Lie type; MSC (2000); 57M12; 57M50; 57M60; 57S17; 20C05; 20C33

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2004
• Tom: 2
• Numer: 2
• Strony: 218-249

Daty

wydano

2004-04-01

online

2004-04-01

Twórcy

autor

Masahito Toda

• Ochanomizu University

Bibliografia

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Identyfikatory

DOI

10.2478/BF02476541