Geometric quasi-isometric embeddings into Thompson's group F

摘要

We use geometric techniques to investigate several examplesof quasi-isometrically embedded subgroups of Thompson's group F.Many of these are explored using the metric propertiesof 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 wellas the interplay between its standard finite and infinite presentations.These subgroups include those of the form Fm×Zn, for integral m,n ≧ 0,which were shown to occur as quasi-isometrically embedded subgroups by Burilloand Guba and Sapir.