论文标题
dirac操作员在刺激双曲线歧管上
The Dirac operator on cusped hyperbolic manifolds
论文作者
论文摘要
我们研究有限体积双曲线n-manifolds上的自旋结构如何限制在尖端上。当尖端横截面是（n-1）-torus时，基本上有两种可能的行为：自旋结构是边界或谎言。我们表明，在每个维度n中，都有至少一个尖头谎言的示例，在每个维度n <= 8中，都有所有尖端都在界限的示例。 通过C. Bar的工作，这意味着Dirac Operator的频谱在第一种情况下为R，在第二种情况下是离散的。因此，我们推断出有垂直双曲线歧管，其狄拉克操作员的频谱在所有维度上，并且其频谱在所有维度n <= 8中都是离散的。
We study how the spin structures on finite-volume hyperbolic n-manifolds restrict to cusps. When a cusp cross-section is a (n-1)-torus, there are essentially two possible behaviours: the spin structure is either bounding or Lie. We show that in every dimension n there are examples where at least one cusp is Lie, and in every dimension n <= 8 there are examples where all the cusps are bounding. By work of C. Bar, this implies that the spectrum of the Dirac operator is R in the first case, and discrete in the second. We therefore deduce that there are cusped hyperbolic manifolds whose spectrum of the Dirac operator is R in all dimensions, and whose spectrum is discrete in all dimensions n <= 8.
