论文标题
鲍威尔在$ s^3 $的Goeritz Group上的猜想是稳定的
Powell's Conjecture on the Goeritz group of $S^3$ is stably true
论文作者
论文摘要
1980年，J。Powell提出，对于每个属$ g $，都足以生成Goeritz Group $ \ Mathcal {G} _g $ g $ g $ g $ Heegaard分裂的五个特定要素。鲍威尔（Powell）的猜想仍然不确定，以$ g \ geq 4 $。令$ \ Mathcal {p} _g \ subset \ Mathcal {g} _g $表示鲍威尔元素生成的子组。在这里，我们证明，对于每个属$ g $，自然函数$ \ Mathcal {g} _g \ to \ Mathcal {g} _ {g+1}/\ Mathcal {p} _ {g+1} $是Trivial。
In 1980 J. Powell proposed that, for every genus $g$, five specific elements suffice to generate the Goeritz group $\mathcal {G}_g$ of genus $g$ Heegaard splittings of $S^3$. Powell's Conjecture remains undecided for $g \geq 4$. Let $\mathcal{P}_g \subset \mathcal {G}_g$ denote the subgroup generated by Powell's elements. Here we show that, for each genus $g$, the natural function $\mathcal {G}_g \to \mathcal {G}_{g+1}/\mathcal {P}_{g+1}$ is trivial.
