论文标题
自由循环空间上的cartan calculi
Cartan calculi on the free loop spaces
论文作者
论文摘要
cartan演算的一个典型例子是谎言衍生物和de rham复合物衍生环上歧管的矢量场的收缩。在此手稿中，研究了cartan演算的第二阶段。在一般环境中，该阶段是由André-Quillen的共同学获得的操作员，该阶段是在Hochschild同源性的$ a $ A $ A $ a $ a $ a $ a $方面的同型cartan cyculus的hochschild同源性方面获得的。此外，卡坦微积分是通过从$ m $ $ m $的循环共同体中的space $ m $上的自我动力$ M $上的自我动力元素等效的理性同型组的地图来解释的。我们还通过$γ_1$ MAP，由于Félix和Thomas，将Sullivan的同构文字提供了几何描述，将Sullivan的同构与代数carculus与代数相关。
A typical example of a Cartan calculus consists of the Lie derivative and the contraction with vector fields of a manifold on the derivation ring of the de Rham complex. In this manuscript, a second stage of the Cartan calculus is investigated. In a general setting, the stage is formulated with operators obtained by the André-Quillen cohomology of a commutative differential graded algebra $A$ on the Hochschild homology of $A$ in terms of the homotopy Cartan calculus in the sense of Fiorenza and Kowalzig. Moreover, the Cartan calculus is interpreted geometrically with maps from the rational homotopy group of the monoid of self-homotopy equivalences on a space $M$ to the derivation ring on the loop cohomology of $M$. We also give a geometric description to Sullivan's isomorphism, which relates the geometric Cartan calculus to the algebraic one, via the $Γ_1$ map due to Félix and Thomas.
