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Daryl Cooper and Darren D. Long 1. Trimming

Summary: Trimming
Daryl Cooper and Darren D. Long
1. Trimming
2. Some Examples
Both authors were supported in part by the NSF.
We consider the question of deciding whether or not certain
subgroups of certain cocompact Kleinian groups are geometri-
cally finite or infinite. This is reduced to a question about sim-
ilarity interval exchange maps. The concept of trimming pro-
duces an practical algorithm to settle the latterquestion. This
algorithm has been implemented on a computer and the re-
sults are perplexing.
In Cooper et al. 1997], we described an algo-
rithm to determine whether a certain kind of sur-
face in a three-manifold is quasifuchsian or a vir-
tual bre. The surface in question is required to
be transverse to the suspension ow in a closed hy-
perbolic three-manifold which bres, but need not


Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara


Collections: Mathematics