A proof that Thompson's groups have infinitely many relative ends
نویسندگان
چکیده
منابع مشابه
A Proof That Thompson’s Groups Have Infinitely Many Relative Ends
We show that each of Thompson’s groups F , T , and V has infinitely many ends relative to the groups F[0,1/2], T[0,1/2], and V[0,1/2) (respectively). As an application, we simplify the proof, due to Napier and Ramachandran, that F , T , and V are not Kähler groups. We go on to show that Thompson’s groups T and V have Serre’s property FA. The main theorems together answer a question on Bestvina’...
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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 correspond...
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ژورنال
عنوان ژورنال: Journal of Group Theory
سال: 2011
ISSN: 1433-5883,1435-4446
DOI: 10.1515/jgt.2010.068