Artin堆范畴中的循环运算与引力相关子
A Cyclic Operad in the Category of Artin Stacks and Gravitational Correlators
摘要：
我们定义了一个Artin堆栈，它可以被认为是亏格为零的稳定两点曲线的不存在（或空）模空间的替代物。我们表明，这个Artin堆栈可以被看作是首项的循环操作符的堆栈类别。应用同调函子，我们得到一个线性循环算子。我们用公式证明了光滑射影簇的上同调在这个同调运算上具有代数结构，并且引力量子上同调可以用这个代数自然地表示.作为对这些公式的检验，我们展示了如何从这些公式中推导出引力差之间的某些众所周知的关系。
英文摘要：
We define an Artin stack which may be considered as a substitute for the non-existing (or empty) moduli space of stable two-pointed curves of genus zero. We show that this Artin stack can be viewed as the first term of a cyclic operad in the category of stacks. Applying the homology functor we obtain a linear cyclic operad. We formulate conjectures which assert that cohomology of a smooth projective variety has the structure of an algebra over this homology operad and that gravitational quantum cohomology can naturally expressed in terms of this algebra. As a test for these conjectures we show how certain well-known relations between gravitational correlators can be deduced from them.
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