论文标题
DG Hopf Cooperads的映射空间和同型自动化$ e_n $ -operads的合理化
Mapping Spaces for DG Hopf Cooperads and Homotopy Automorphisms of the Rationalization of $E_n$-operads
论文作者
论文摘要
我们定义了对差分级别的霍普夫·库拉德斯（简称DG Hopf Cooperads的类别）类别的简单丰富。我们证明，我们的简单富集部分满足了DG Hopf Cooperads类别的简单模型类别结构的公理。我们使用这种简单的模型结构来定义DG Hopf Cooperads类别中的映射空间模型，并通过处理简单的单体结构来升级有关DG Hopf Cooperads同型自动形态空间的文献结果。理性同遵循的统一理论意味着，DG Hopf Cooperads的同型自动形态空间可以被视为拓扑空间（或在SimpleCicial集合）中合理化的手术合理化的同型自动化空间的模型。作为一个主要应用，我们证明了莫拉尔 - 卡丹在kontsevich图复合体上的空间代数是同质的，在简单的单体类别中，与小迪斯特人的合理性的同型自动型自动化空间相当。
We define a simplicial enrichment on the category of differential graded Hopf cooperads (the category of dg Hopf cooperads for short). We prove that our simplicial enrichment satisfies, in part, the axioms of a simplicial model category structure on the category of dg Hopf cooperads. We use this simplicial model structure to define a model of mapping spaces in the category of dg Hopf cooperads and to upgrade results of the literature about the homotopy automorphism spaces of dg Hopf cooperads by dealing with simplicial monoid structures. The rational homotopy theory of operads implies that the homotopy automorphism spaces of dg Hopf cooperads can be regarded as models for the homotopy automorphism spaces of the rationalization of operads in topological spaces (or in simplicial sets). We prove, as a main application, that the spaces of Maurer--Cartan forms on the Kontsevich graph complex Lie algebras are homotopy equivalent, in the category of simplicial monoids, to the homotopy automorphism spaces of the rationalization of the operads of little discs.
