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~k 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 combable nor has a regular language of geodesics. Additionally, we prove that dead ends (or k-pockets) exist in F(N) with respect to X and all have depth 2. A dead end w is a word for which no geodesic path in the Cayley graph Γ which passes through w can continue past w, and the depth of w is the minimal m ∈ N such that a path of length m+1 existsbeginning at w and leaving B_(w). We represent elements of F(N) by tree-pair diagrams so that we can use Fordham's method for computing word length. This paper generalizes results by Cleary and Taback, who proved the case N = 2.
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