论文标题
具有四个理性缠结的蒙特西诺诺斯结中的封闭基本表面的数量
The Number of Closed Essential Surfaces in Montesinos Knots with Four Rational Tangles
论文作者
论文摘要
在具有4个合理缠结的双曲线蒙特西尼诺斯结的补充中，我们研究了固定属$ g $的封闭，连接，必不可少的，定向的表面，直到同位素。我们表明，恰好有12个属2个表面和$ 8ϕ（g -1）$属的$大于2的表面，其中$ ϕ（g -1）$是$ g -1 $的Euler Toctient函数。观察到该计数与结的交叉数无关。此外，这类结构成了无限类的双曲线3个manifolds，结果适用于所有此类结的补充。
In the complement of a hyperbolic Montesinos knot with 4 rational tangles, we investigate the number of closed, connected, essential, orientable surfaces of a fixed genus $g$, up to isotopy. We show that there are exactly 12 genus 2 surfaces and $8ϕ(g - 1)$ surfaces of genus greater than 2, where $ϕ(g - 1)$ is the Euler totient function of $g - 1$. Observe that this count is independent of the number of crossings of the knot. Moreover, this class of knots form an infinite class of hyperbolic 3-manifolds and the result applies to all such knot complements.
