Higher dimensional Thompson groups have subgroups with infinitely many relative ends
Motoko Kato · arXiv (Cornell University) · 2015
The Thompson group V is a subgroup of the homeomorphism group of the Cantor set. Brin defined higher dimensional Thompson groups nV as generalizations of V. We prove that the number of ends of nV is equal to 1, and there are subgroups such that the relative number of ends are infinite. This is a generalization of the corresponding result of Farley, who studied V.