Seesaw words in Thompson's group F

Abstract

We describe a family of words in Thompson's group F which present a challenge to the question of finding canonical minimal length representatives, and which show that F is not combable by geodesics. These words have the property that there are only two possible suffixes of long lengths for geodesic paths to the word from the identity; one is of the form $g^k$ and the other of the form $g^{-k}$ where g is a generator of the group.

11 pages, 6 figures

Cited by in corpus (2)

• Cone types and geodesic languages for lamplighter groups and Thompson's group F
• Unusual Geodesics in generalizations of Thompson's Group F