论文标题
更高的谎言理论
Higher Lie theory
论文作者
论文摘要
我们提出了一种新颖的方法，即通过将Maurer-Cartan太空函数用通用的cosimimplicial对象代表毛勒 - 卡丹太空函数来整合同质副本的问题。这恢复了Getzler的原始函数，但允许我们证明存在其他以前未知的结构和属性。也就是说，我们引入了一个举止良好的左伴函子，我们建立了有关无限型的函数性，并构建了高级贝克 - 贝克贝克贝尔 - 霍斯多夫公式的连贯层次结构。多亏了这些工具，我们才能够建立更高谎言理论的最重要结果。我们使用了最新的经营微积分的发展，这使我们在所有阶段都明确了树木的公式。我们通过将该理论应用于理性同义理论来结束：证明左伴函子为我们提供同型谎言代数模型，以忠实地捕获其理性同义类型。
We present a novel approach to the problem of integrating homotopy Lie algebras by representing the Maurer-Cartan space functor with a universal cosimplicial object. This recovers Getzler's original functor but allows us to prove the existence of additional, previously unknown, structures and properties. Namely, we introduce a well-behaved left adjoint functor, we establish functoriality with respect to infinity-morphisms, and we construct a coherent hierarchy of higher Baker-Campbell-Hausdorff formulas. Thanks to these tools, we are able to establish the most important results of higher Lie theory. We use the recent developments of the operadic calculus, which leads us to explicit tree-wise formulas at all stage. We conclude by applying this theory to rational homotopy theory: the left adjoint functor is shown to provide us with homotopy Lie algebra models for topological spaces which faithfully capture their rational homotopy type.
