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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

Classifying torsion-free subgroups of the Picard group


Authors: Andrew M. Brunner, Michael L. Frame, Youn W. Lee and Norbert J. Wielenberg
Journal: Trans. Amer. Math. Soc. 282 (1984), 205-235
MSC: Primary 57N10; Secondary 11F06, 20F38, 22E40, 57M25, 57S30
MathSciNet review: 728710
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Abstract: Torsion-free subgroups of finite index in the Picard group are the fundamental groups of hyperbolic $ 3$-manifolds. The Picard group is a polygonal product of finite groups. Recent work by Karrass, Pietrowski and Solitar on the subgroups of a polygonal product make it feasible to calculate all the torsion-free subgroups of any finite index. This computation is carried out here for index 12 and 24, where there are, respectively, 2 and 17 nonisomorphic subgroups. The manifolds are identified by using surgery.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0728710-2
PII: S 0002-9947(1984)0728710-2
Article copyright: © Copyright 1984 American Mathematical Society