论文标题
琴弦拓扑的霍奇分解
Hodge decomposition of string topology
论文作者
论文摘要
令$ x $为简单连接的封闭式椭圆形同型类型的封闭式歧管。我们证明了$ s^1 $ -Equivariant同源性$ \ OVERLINE { $ \ OVILLINE {H} _ {\ AST}^{s^1}（\ Mathcal {l} X，\ Mathbb {Q}）$，使其成为一个大的lie代数。我们根据对同源性nilpotent有限二维DG的普遍包围代数的普遍包围代数的衍生泊松结构的一般定理推断出这一结果。我们的定理解决了我们早期工作中提出的猜想。
Let $X$ be a simply connected closed oriented manifold of rationally elliptic homotopy type. We prove that the string topology bracket on the $S^1$-equivariant homology $\overline{H}_{\ast}^{S^1}(\mathcal{L}X,\mathbb{Q}) $ of the free loop space of $X$ preserves the Hodge decomposition of $\overline{H}_{\ast}^{S^1}(\mathcal{L}X,\mathbb{Q}) $ , making it a bigraded Lie algebra. We deduce this result from a general theorem on derived Poisson structures on the universal enveloping algebras of homologically nilpotent finite-dimensional DG Lie algebras. Our theorem settles a conjecture proposed in our earlier work.
