Geometric quasi-isometric embeddings into Thompson's group F

Details Geometric quasi-isometric embeddings into Thompson's group F Geometric quasi-isometric embeddings into Thompson's group F

2002-11-15

arxiv.org/abs/math/0211243v2

Mathematics

Group Theory

11 pages, 8 figures

Scientific paper

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 phi 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 standard finite and infinite presentations. These subgroups include those of the form F^m cross Z^n, for integral non-negative m and n, which were shown to occur as quasi-isometrically embedded subgroups by Burillo and Guba and Sapir.

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