The Dehn function of Richard Thompson's group $T$

TL;DR

This paper improves the upper bound on the Dehn function of Richard Thompson's group T from polynomial degree 7 to degree 5, advancing understanding of its geometric properties.

Contribution

It establishes a tighter polynomial upper bound on the Dehn function of group T, refining previous results by V.S. Guba.

Findings

Dehn function of T is bounded above by n^5

Improves previous bound of n^7

Contributes to understanding of T's geometric properties

Abstract

V.S.Guba had proved that the R.Thompson group $T$ satisfies polynomial isoperimetric inequality and $\Phi_T(n)\preceq n^7$, where $\Phi_T$ is the Dehn function of group $T$. In this paper, we show that $\Phi_T(n)\preceq n^5$.