Formality of Kapranov's brackets in K\"ahler geometry via pre-Lie deformation theory
Formality of Kapranov's brackets in K\"ahler geometry via pre-Lie deformation theory
复制标题
DOI：
10.1093/imrn/rnv362
复制
发表时间：
2013-07
期刊：
影响因子：
--
通讯作者：
R. Bandiera
中科院分区：
文献类型：
--
作者：
R. Bandiera
We recover some recent results by Dotsenko, Shadrin and Vallette on the Deligne groupoid of a pre-Lie algebra, showing that they follow naturally by a pre-Lie variant of the PBW Theorem. As an application, we show that Kapranov's $L_\infty$ algebra structure on the Dolbeault complex of a K\"ahler manifold is homotopy abelian and independent on the choice of K\"ahler metric up to an $L_\infty$ isomorphism, by making the trivializing homotopy and the $L_\infty$ isomorphism explicit.
