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


On Klein's combination theorem. IV

Author: Bernard Maskit
Journal: Trans. Amer. Math. Soc. 336 (1993), 265-294
MSC: Primary 30F40
MathSciNet review: 1137258
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Abstract: This paper contains an expansion of the combination theorems to cover the following problems. New rank $ 1$ parabolic subgroups are produced, while, as in previous versions, all elliptic and parabolic elements are tracked. A proof is given that the combined group is analytically finite if and only if the original groups are; in the analytically finite case, we also give a formula for the hyperbolic area of the combined group (i.e., the hyperbolic area of the set of discontinuity on the $ 2$-sphere modulo $ G$) in terms of the hyperbolic areas of the original groups. There is also a new variation on the first combination theorem in which the common subgroup has finite index in one of the two groups.

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PII: S 0002-9947(1993)1137258-0
Article copyright: © Copyright 1993 American Mathematical Society