Diagram Groups
نویسنده
چکیده
منابع مشابه
On subgroups of R. Thompson’s group F and other diagram groups
In this paper, we continue our study of the class of diagram groups. Simply speaking, a diagram is a labelled plane graph bounded by a pair of paths (the top path and the bottom path). To multiply two diagrams, one simply identifies the top path of one diagram with the bottom path of the other diagram, and removes pairs of “reducible” cells. Each diagram group is determined by an alphabet X, co...
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In this paper, we introduce the concept of the independence graph of a directed 2-complex. We show that the class of diagram groups is closed under graph products over independence graphs of rooted 2-trees. This allows us to show that a diagram group containing all countable diagram groups is a semi-direct product of a partially commutative group and R. Thompson's group F. As a result, we prove...
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Hughes defined a class of groups that act as local similarities on compact ultrametric spaces. Guba and Sapir had previously defined braided diagram groups over semigroup presentations. The two classes of groups share some common characteristics: both act properly by isometries on CAT(0) cubical complexes, and certain groups in both classes have type F∞, for instance. Here we clarify the relati...
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We prove that all diagram groups (in the sense of Guba and Sapir) are left-orderable. The proof is in two steps: firstly, it is proved that all diagram groups inject in a certain braid group on infinitely many strings, and secondly, this group is then shown to be left-orderable.
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In this paper, we show that a class of 2-dimensional locally CAT(-1) spaces is topologically rigid: isomorphism of the fundamental groups is equivalent to the spaces being homeomorphic. An immediate application of this result is a diagram rigidity theorem for certain amalgamations of free groups. The direct limit of two such amalgamations are isomorphic if and only if there is an isomorphism be...
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