The Dehn Function Of Richard Thompson's Group T

The groups F,T and V,where F<T<V,were discovered by Richard Thompson in the 1960s.The group F is torsion-free;it was used to construct some finitely presented groups with unsolvable word problem.The group T has elements of all orders.It was the first example of an infinite,finitely presented simple group.Guba has proved that the Dchn function of Richard Thompson's group F is quadratic.We improve Guba's result about the Dehn function of R.Thompson's group T by constructing refinement van Kampen diagrams.Guba has proved that the Dehn function of R.Thompson's group T has a polynomial upper bound,namely,?T(n)? n7,which can be found in article[27].We improve it to ?T(n)?n5.