论文标题
在inoue表面的光谱集上
On the spectral sets of Inoue surfaces
论文作者
论文摘要
inoue表面是某些非kaehler复合物表面，在圆上具有$ t^3 $束的结构。我们使用Tricerri度量标准和规范旋转$^c $结构来研究inoue表面$ s_m $，以及相应的手性狄拉克运算符，由平坦的$ \ mathbb c^*$ - 连接扭曲。扭曲连接由\ Mathbb c^*$中的$ z \确定，而扭曲的狄拉克运算符$ \ Mathcal d^{\ pm} _z $的点不可交换称为光谱点。我们表明，环内没有光谱点$α^{ - 1/4} <| z | <α^{1/4} $，其中$α> 1 $是矩阵$ m $的唯一真实特征值，它决定$ s_m $，并在其边界上找到频谱点。通过Taubes的最终周期性操作员理论，这意味着相应的Dirac操作员是弗雷德·霍尔姆（Fredholm），在任何最终的周期歧管上，其最终以$ s_m $为模型。
The Inoue surfaces are certain non-Kaehler complex surfaces that have the structure of a $T^3$ bundle over the circle. We study the Inoue surfaces $S_M$ with the Tricerri metric and the canonical spin$^c$ structure, and the corresponding chiral Dirac operators twisted by a flat $\mathbb C^*$--connection. The twisting connection is determined by $z \in \mathbb C^*$, and the points for which the twisted Dirac operators $\mathcal D^{\pm}_z$ are not invertible are called spectral points. We show that there are no spectral points inside the annulus $α^{-1/4} < |z| < α^{1/4}$, where $α>1$ is the only real eigenvalue of the matrix $M$ that determines $S_M$, and find the spectral points on its boundary. Via Taubes' theory of end-periodic operators, this implies that the corresponding Dirac operators are Fredholm on any end-periodic manifold whose end is modeled on $S_M$.
