Thompson群V的Dehn函数至多为六次
The Dehn function of Thompson's group $V$ is at most sextic
AI总结：
本文将Thompson群V的Dehn函数上界从n¹¹改进为n⁶，同时通过显式van Kampen图探究其关系复杂性，补充了Thompson群Dehn函数的相关研究进展。
AI中文摘要：
Guba的一项重要结果表明，Thompson群F的Dehn函数是二次的（《Inv. Math.》163:313-342）；在另一篇论文（《Alg. prob. in Grps. and Semigrps》，91-120）中，Guba证明Thompson群T和V的Dehn函数上界分别为n⁷和n¹¹。近期Migliorini证明Thompson群T的Dehn函数也为二次（《For. of Math. Sigma》13:e109）。本文将Thompson群V的Dehn函数上界改进为n⁶，并通过显式van Kampen图探究其关系的复杂性。
英文摘要：
A remarkable result of Guba shows that the Dehn function of Thompson's group $F$ is quadratic (Inv. Math. 163:313-342). In another paper (Alg. prob. in Grps. and Semigrps, 91-120), Guba showed that Thompson's group $T$ and $V$ have Dehn functions bounded above by $n^7$ and $n^{11}$, respectively. Recently, Migliorini showed that the Dehn function of Thompson's group $T$ is also quadratic (For. of Math. Sigma, 13:e109). In this paper, we improve the upper bound of the Dehn function of Thompson's group $V$ to $n^6$ and explore the intricacies of its relations via explicit van Kampen diagrams.
