论文标题
通过琐碎的表面节结获得的三触
Trisections obtained by trivially regluing surface-knots
论文作者
论文摘要
令$ s $为$ p^2 $ -knot，它是带有正常欧拉数为0的2结的连接总和，而无效的Euler Number Number $ \ pm2 $在带有Trisection $ T_ {X} $的无效的欧拉数$ \ pm2 $中。然后，我们表明，$ \叠加{ν（s）} $和$ x-ν（s）$获得的$ x $的三角$ x $与$ t_ {x} $的稳定性相差。应该注意的是，此结果并不明显，因为Kim和Miller引入的边界稳定性用于构建$ X-ν（S）$的相对分解。作为推论，如果$ x = s^4 $，则由此产生的三角形是稳定$ s^4 $的稳定。该结果与猜想是Waldhausen关于Heegaard分裂的4维类似物的猜想。
Let $S$ be a $P^2$-knot which is the connected sum of a 2-knot with normal Euler number 0 and an unknotted $P^2$-knot with normal Euler number $\pm2$ in a closed 4-manifold $X$ with trisection $T_{X}$. Then, we show that the trisection of $X$ obtained by the trivial gluing relative trisections of $\overline{ν(S)}$ and $X-ν(S)$ is diffeomorphic to a stabilization of $T_{X}$. It should be noted that this result is not obvious since boundary-stabilizations introduced by Kim and Miller are used to construct a relative trisection of $X-ν(S)$. As a corollary, if $X=S^4$, the resulting trisection is diffeomorphic to a stabilization of the genus 0 trisection of $S^4$. This result is related to the conjecture that is a 4-dimensional analogue of Waldhausen's theorem on Heegaard splittings.
