Introduction to the Intersection Theory for Twisted Homology and Cohomology Groups
Introduction to the Intersection Theory for Twisted Homology and Cohomology Groups
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扭曲同调群和上同调群的交集理论简介
DOI：
10.22323/1.383.0007
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发表时间：
2022
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通讯作者：
Keiji Matsumoto
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作者：
Keiji Matsumoto
我们介绍了与超几何函数的欧拉型积分相关的扭曲同调群和上同调群的交集理论。我们引入由扭曲斯托克斯定理驱动的扭曲同调群和上同调群，并给出它们的维数公式。我们定义了扭曲同调群之间的交集形式和扭曲上同调群之间的交集形式，并解释了如何计算它们。这些交叉形式与扭曲同调群和上同调群之间的自然配对兼容。这种兼容性产生了一种扭曲的周期关系，它将交集数和被视为某种超几何函数的周期积分联系起来。在附录中，我们证明了艾略特的恒等式可以从扭曲的周期关系中获得。
We give an introduction to the intersection theory for twisted homology and cohomology groups associated with Euler type integrals of hypergeometric functions. We introuduce twisted homology and cohomology groups motivated by Twisted Stokes’ Theorem, and give their dimension formulas. We define an intersection form between twisted homology groups and that between twisted cohomology groups, and explain how to compute them. These intersection forms are compatible with the natural pairing between the twisted homology and cohomology groups. This compatibility yields a twisted period relation, which relates intersection numbers and period integrals regarded as some kinds of hypergeometric functions. In Appendix, we show that Elliott’s identity can be obtained from the twisted period relation.
K.Matsumoto：“超几何函数的对偶性和不变高斯-马宁系统”复合数学。
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