Seesaw words in Thompson’s group F
نویسنده
چکیده
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 and the other of the form g where g is a generator of the group.
منابع مشابه
Unusual Geodesics in Generalizations of Thompson’s Group F
We prove that seesaw words exist in Thompson’s Group F (N) for N = 2, 3, 4, ... with respect to the standard finite generating set X. A seesaw word w with swing k has only geodesic representatives ending in g or g−k (for given g ∈ X) and at least one geodesic representative of each type. The existence of seesaw words with arbitrarily large swing guarantees that F (N) is neither synchronously co...
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تاریخ انتشار 2008