The Automorphism Group of Thompson’s Group F : Subgroups and Metric Properties
نویسنده
چکیده
We describe some of the geometric properties of the automorphism group Aut(F ) of Thompson’s group F . We give realizations of Aut(F ) geometrically via periodic tree pair diagrams, which lead to natural presentations and give effective methods for estimating the word length of elements. We study some natural subgroups of Aut(F ) and their metric properties. In particular, we show that the subgroup of inner automorphisms of F is at least quadratically distorted in Aut(F ), whereas other subgroups of Aut(F ) isomorphic to F are undistorted.
منابع مشابه
Metric Properties of the Braided Thompson’s Groups
Braided Thompson’s groups are finitely presented groups introduced by Brin and Dehornoy which contain the ordinary braid groups Bn, the finitary braid group B∞ and Thompson’s group F as subgroups. We describe some of the metric properties of braided Thompson’s groups and give upper and lower bounds for word length in terms of the number of strands and the number of crossings in the diagrams use...
متن کاملGeometric quasi-isometric embeddings into Thompson's group F
We use geometric techniques to investigate several examples of quasi-isometrically embedded subgroups of Thompson’s group F . Many of these are explored using the metric properties of the shift map φ in F . These subgroups have simple geometric but complicated algebraic descriptions. We present them to illustrate the intricate geometry of Thompson’s group F as well as the interplay between its ...
متن کاملGroup laws and free subgroups in topological groups
We prove that a permutation group in which different finite sets have different stabilizers cannot satisfy any group law. For locally compact topological groups with this property we show that almost all finite subsets of the group generate free subgroups. We derive consequences of these theorems on Thompson’s group F , weakly branch groups, automorphism groups of regular trees and profinite gr...
متن کاملCombinatorial and Metric Properties of Thompson’s Group T
We discuss metric and combinatorial properties of Thompson’s group T , including normal forms for elements and unique tree pair diagram representatives. We relate these properties to those of Thompson’s group F when possible, and highlight combinatorial differences between the two groups. We define a set of unique normal forms for elements of T arising from minimal factorizations of elements in...
متن کاملMetrics and Embeddings of Generalizations of Thompson’s Group F
The distance from the origin in the word metric for generalizations F (p) of Thompson’s group F is quasi-isometric to the number of carets in the reduced rooted tree diagrams representing the elements of F (p). This interpretation of the metric is used to prove that every F (p) admits a quasiisometric embedding into every F (q), and also to study the behavior of the shift maps under these embed...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011