Forest diagrams for elements of Thompson's group F

Details Forest diagrams for elements of Thompson's group F Forest diagrams for elements of Thompson's group F

2003-05-28

arxiv.org/abs/math/0305412v1

Mathematics

Group Theory

44 pages, 70 figures

Scientific paper

We introduce forest diagrams to represent elements of Thompson's group F. These diagrams relate to a certain action of F on the real line in the same way that tree diagrams relate to the standard action of F on the unit interval. Using forest diagrams, we give a conceptually simple length formula for elements of F with respect to the {x_0,x_1} generating set, and we discuss the construction of minimum-length words for positive elements. Finally, we use forest diagrams and the length formula to examine the structure of the Cayley graph of F.

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