论文标题
$ \ mathrm {su}（3）$的几何形状 - 圆环结的字符品种
Geometry of $\mathrm{SU}(3)$-character varieties of torus knots
论文作者
论文摘要
我们描述了结组$γ_{m，n} = \ langle x，y | x^n = y^m \ rangle $纳入组$ \ mathrm {surm {su}（3）$，通过将角色品种分类为完全还原的表示形式，分解为$ 2 $数值的表示形式，并分解为$ 1 $ $ $的表示，以及两种类型的依赖于两种类型的代表，是否依赖于两种类型的代表，依赖于两种类型的范围。矩阵具有一个特征值$ 2 $。我们描述了每个层的闭合如何符合较低的地层，并使用它来计算紧凑的欧拉（Euler）特征，并证明将$ \ mathrm {su}（3）$包含在$ \ mathrm {Slrm {Slrm {sl}（3，\ Mathbb {c}）$的角色中。
We describe the geometry of the character variety of representations of the knot group $Γ_{m,n}=\langle x,y| x^n=y^m\rangle$ into the group $\mathrm{SU}(3)$, by stratifying the character variety into strata correspoding to totally reducible representations, representations decomposing into a $2$-dimensional and a $1$-dimensional representation, and irreducible representations, the latter of two types depending on whether the matrices have distinct eigenvalues, or one of the matrices has one eigenvalue of multiplicity $2$. We describe how the closure of each stratum meets lower strata, and use this to compute the compactly supported Euler characteristic, and to prove that the inclusion of the character variety for $\mathrm{SU}(3)$ into the character variety for $\mathrm{SL}(3,\mathbb{C})$ is a homotopy equivalence.
