Filling Length in Finitely Presentable Groups
نویسندگان
چکیده
Filling length measures the length of the contracting closed loops in a null-homotopy. The filling length function of Gromov for a finitely presented group measures the filling length as a function of length of edge-loops in the Cayley 2-complex. We give a bound on the filling length function in terms of the log of an isoperimetric function multiplied by a (simultaneously realisable) isodiametric function. 1 Isoperimetric and isodiametric functions Given a finitely presented group Γ = 〈A |R〉 various filling invariants arise from considering reduced words w in the free group F (A) such that w =Γ 1. Such null-homotopic words are characterised by the existence of an equality in F (A)
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