论文标题
弯曲$ l_ \ infty $ - algebras中存在毛勒 - 卡丹元素的障碍理论，以及$ p_ \ infty $ -algebras的固有形式的应用
An Obstruction Theory for the Existence of Maurer-Cartan Elements in curved $L_\infty$-algebras and an Application in Intrinsic Formality of $P_\infty$-Algebras
论文作者
论文摘要
令$ \ mathfrak {g} $为弯曲的$ l_ \ infty $ -Algebra，并带有完整的过滤$ \ mathfrak {f} \ Mathfrak {g} $。假设存在一个整数$ r \ in \ mathbb {n} _0 $，曲率$μ_0$满足$μ_0\ in \ mathfrak {f} _ {f} _ {2r+1} \ mathfrak {g} $ P+Q = 2 $。我们证明那时莫拉尔 - 卡丹元素就存在。此外，我们表明，作为典型应用程序，对于$ p $，可能是不均匀的koszul Operad，其产生含量为1,2（例如$ p $ = com = com，as，bv，lie，lie，ger），$ p_ \ infty $ -Algebra $ a $是内在形式的，如果它具有内在形式的形式，则$ \ mathrm {def}（h（a）\ stackrel {\ mathrm {id}}} {\ to} h（a））$在总数1中是acyclic。
Let $\mathfrak{g}$ be a curved $L_\infty$-algebra endowed with a complete filtration $\mathfrak{F}\mathfrak{g}$. Suppose there exists an integer $r \in \mathbb{N}_0$ for which the curvature $μ_0$ satisfies $μ_0 \in \mathfrak{F}_{2r+1} \mathfrak{g}$ and the spectral sequence yields $E_{r+1}^{p,q} =0$ for $p,q$ with $p+q=2$. We prove that then a Maurer-Cartan element exists. In addition, we show, as a typical application, that for $P$ a possibly inhomogeneous Koszul operad with generating set in arities 1,2 (e.g. $P$=Com,As,BV,Lie,Ger), a $P_\infty$-algebra $A$ is intrinsically formal if its twisted deformation complex $\mathrm{Def}(H(A)\stackrel{\mathrm{id}}{\to} H(A))$ is acyclic in total degree 1.
