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Seesaw words in Thompson's group F

Sean Cleary·Jennifer Taback
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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.

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Sean Cleary, Jennifer Taback. 2004-08-02. Seesaw words in Thompson's group F. https://arxiv.org/abs/math/0310466

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