2 5 A pr 2 01 5 Higher dimensional Thompson groups have subgroups with infinitely many relative ends
نویسندگان
چکیده
The Thompson group V is a subgroup of the homeomorphism group of the Cantor set C. Brin [3] defined higher dimensional Thompson groups nV as generalizations of V . For each n, nV is a subgroup of the homeomorphism group of Cn. We prove that the number of ends of nV is equal to 1, and there is a subgroup of nV such that the relative number of ends is ∞. This is a generalization of the corresponding result of Farley [8], who studied the Thompson group V . As a corollary, nV has the Haagerup property and is not a Kähler group.
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