On Klein’s combination theorem. IV
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- by Bernard Maskit PDF
- Trans. Amer. Math. Soc. 336 (1993), 265-294 Request permission
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.References
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Additional Information
- © Copyright 1993 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 336 (1993), 265-294
- MSC: Primary 30F40
- DOI: https://doi.org/10.1090/S0002-9947-1993-1137258-0
- MathSciNet review: 1137258