发表机构
Southwest Jiaotong University（西南交通大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为有限定向折叠商构造实de Rham实现，定义实Chen-Hu代数，识别相位障碍类，并证明相位平凡情形下存在包含Chen-Hu偶扇区的典范结合分次上同调代数，对Eisenstein阿贝尔曲面给出16维Frobenius代数显式结构。
AI 中文摘要
本文研究有限定向折叠商的de Rham实现。对于几乎复全局商的保向惯性，我们在Chen-Hu代数上构造了一个反线性对合，其固定子代数是Chen-Ruan代数的一个实形式。对于真正的反向固定扇区，我们证明了不存在坐标不变的单一扇区分数年龄。当Calabi-Yau体积线被保持时，相对相位定义了一个典范类$[\mu_{\mathbb R}]\in H^2(\widehat G;\mathbb Z_\epsilon)$。我们将此类与相干实相位提升的Bockstein障碍等同起来，并证明其消失等价于（在重新调整体积形式后）相位平凡的定向折叠作用。然后，我们利用相对Fredholm丛和行列式线缝合，制定了一个一般的Euler-Gysin实现定理。对于相位平凡的Calabi-Yau曲面，我们直接验证了可容许性条件，并获得了包含Chen-Hu偶扇区和奇固定曲面的典范定义的结合分次上同调代数。对于具有六阶二面体作用的Eisenstein阿贝尔曲面，我们显式计算了中心化子不变代数；它是一个16维Frobenius代数，其奇扇区乘法在移位分次中是非交换的。我们还解释了与早期无向轨道上同调构造的关系。
英文摘要
In this paper, we study de Rham realizations for finite orientifold quotients. On the orientation preserving inertia of an almost complex global quotient we construct an anti-linear involution of the Chen-Hu algebra whose fixed subalgebra is a real form of the Chen-Ruan algebra. For genuine orientation reversing fixed sectors we prove that no coordinate invariant single sector fractional age exists. When a Calabi-Yau volume line is preserved, the relative phases define a canonical class $[μ_{\mathbb R}]\in H^2(\widehat G;\mathbb Z_ε)$. We identify this class with the Bockstein obstruction to a coherent real phase lift and prove that its vanishing is equivalent, after rephasing the volume form, to a phase trivial orientifold action. We then formulate a general Euler-Gysin realization theorem using relative Fredholm bundles and determinant-line sewing. For phase trivial Calabi-Yau surfaces we verify the admissibility conditions directly and obtain a canonically defined associative graded cohomology algebra containing the Chen-Hu even sector and the odd fixed surfaces. For an Eisenstein abelian surface with an order six dihedral action we compute the centralizer invariant algebra explicitly; it is a $16$ dimensional Frobenius algebra whose odd sector multiplication is noncommutative in the shifted grading. We also explain the relation with earlier unoriented orbifold cohomology constructions.
Comments42 pages. Comments welcome
