论文标题
辅助领域理论的变形理论
Deformation theory of Cohomological Field Theories
论文作者
论文摘要
我们开发了共同体田地理论的变形理论（COHFTS），该理论是作为模块化作战形态的一般变形理论的特殊情况。这导致我们引入了cohft的概念的两个新的自然扩展：同型（结构链级gromov-所必需的不变性）和量子（在Buryak-Rossi的著作中发现了buryak-rossi-rossi on Actemplable Systems的示例）。我们介绍了Kontsevich的Graph Complex的新版本，并在稳定曲线的模量空间上充满了重言式课程。我们使用它来研究一个新的通用变形组，该组通过Merkulov-Willwacher引起的方法自然作用于量子同型cohfts的模量空间。该小组被证明包含了Prounipotent Grothendieck-TeichMüller组和吉维尔人组。
We develop the deformation theory of cohomological field theories (CohFTs), which is done as a special case of a general deformation theory of morphisms of modular operads. This leads us to introduce two new natural extensions of the notion of a CohFT: homotopical (necessary to structure chain-level Gromov--Witten invariants) and quantum (with examples found in the works of Buryak--Rossi on integrable systems). We introduce a new version of Kontsevich's graph complex, enriched with tautological classes on the moduli spaces of stable curves. We use it to study a new universal deformation group which acts naturally on the moduli spaces of quantum homotopy CohFTs, by methods due to Merkulov--Willwacher. This group is shown to contain both the prounipotent Grothendieck--Teichmüller group and the Givental group.
