Quasi-isometrically embedded subgroups of braid and diffeomorphism groups
نویسندگان
چکیده
منابع مشابه
Quasi-isometrically Embedded Subgroups of Braid and Diffeomorphism Groups
We show that a large class of right-angled Artin groups (in particular, those with planar complementary defining graph) can be embedded quasi-isometrically in pure braid groups and in the group Diff(D2, ∂D2, vol) of area preserving diffeomorphisms of the disk fixing the boundary (with respect to the L2-norm metric); this extends results of Benaim and Gambaudo who gave quasi-isometric embeddings...
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The goal of this paper is to construct quasi-isometrically embedded subgroups of Thompson’s group F which are isomorphic to F × Zn for all n. A result estimating the norm of an element of Thompson’s group is found. As a corollary, Thompson’s group is seen to be an example of a finitely presented group which has an infinite-dimensional asymptotic cone. The interesting properties of Thompson’s gr...
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We give criteria for determining the approximate length of elements in any given cyclic subgroup of the Thompson-Stein groups F (n1, ..., nk) such that n1 − 1|ni − 1 ∀i ∈ {1, ..., k} in terms of the number of leaves in the minimal tree-pair diagram representative. This leads directly to the result that cyclic subgroups are quasi-isometrically embedded in the ThompsonStein groups. This result al...
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If G is either a connected Lie group, or a finitely generated solvable group with exponential growth, we show that G contains a quasi-isometrically embedded free sub-semigroup on 2 generators.
متن کاملPure Braid Subgroups of Braided Thompson’s Groups
We describe pure braided versions of Thompson’s group F . These groups, BF and B̂F , are subgroups of the braided versions of Thompson’s group V , introduced by Brin and Dehornoy. Unlike V , elements of F are order-preserving self-maps of the interval and we use pure braids together with elements of F thus preserving order. We define these groups and give normal forms for elements and describe i...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2007
ISSN: 0002-9947
DOI: 10.1090/s0002-9947-07-04332-2