论文标题
古典椒盐脆饼结和左订购性
Classical pretzel knots and left orderability
论文作者
论文摘要
我们考虑经典的椒盐脆饼结$ P（a_1，a_2，a_3）$，其中$ a_1，a_2，a_3 $是正整数。通过使用椭圆形$ \ mathrm {sl} _2（\ mathbb r）$ - 表示的连续路径，我们表明（i）（i）由$ \ frac {m} {l} {l} $ p（$ p（a_1，a_2，a_3）$ $ pluckable und $ \ frac \ frac的3个manifold， （ii）$ n^{\ mathrm {th}} $ - $ p（a_1，a_2，a_3）$的环状分支封面，如果$ n>2π/ \ arccos（1-2/（1 + A_1 A_1 A_1 A_1 A_2 + A_2 + A_2 A_2 A_3 + A_3 + A_3 A_3 A__1），则剩下订购基本组。
We consider the classical pretzel knots $P(a_1, a_2, a_3)$, where $a_1, a_2, a_3$ are positive odd integers. By using continuous paths of elliptic $\mathrm{SL}_2(\mathbb R)$-representations, we show that (i) the 3-manifold obtained by $\frac{m}{l}$-surgery on $P(a_1, a_2, a_3)$ has left orderable fundamental group if $\frac{m}{l} < 1$, and (ii) the $n^{\mathrm{th}}$-cyclic branched cover of $P(a_1, a_2, a_3)$ has left orderable fundamental group if $n > 2π/ \arccos(1-2/(1+a_1 a_2 + a_2 a_3 + a_3 a_1))$.
