标题： 戈德的几何结构变形理论，李理论描述 显示英文标题

标题： Goto's deformation theory of geometric structures, a Lie-theoretical description

摘要： 在\cite{Goto}中，后藤龙志构造了一个配备有一组闭微分形式的流形的形变空间，并表明在一些重要情况下（卡拉比-丘、$G_2$和$Spin(7)$结构），这个形变空间是光滑的。 这一结果统一了关于形变无阻碍性的经典博戈莫洛夫-田刚-托多罗夫定理和乔伊斯定理。 利用Fiorenza和Manetti的工作，我们证明这个形变空间可以作为某个$L_{\infty}$-代数相关的形变空间得到。 我们还证明对于卡拉比-丘、$G_2$和$Spin(7)$结构，这个$L_{\infty}$-代数是同伦交换的。 这给出了Goto定理的新证明。 显示英文摘要

摘要： In \cite{Goto}, Ryushi Goto has constructed the deformation space for a manifold equipped with a collection of closed differential forms and showed that in some important cases (Calabi-Yau, $G_2$- and $Spin(7)$-structures) this deformation space is smooth. This result unifies the classical Bogomolov-Tian-Todorov and Joyce theorems about unobstructedness of deformations. Using the work of Fiorenza and Manetti, we show that this deformation space could be obtained as the deformation space associated to a certain $L_{\infty}$-algebra. We also show that for Calabi-Yau, $G_2$- and $Spin(7)$-structures this $L_{\infty}$-algebra is homotopy abelian. This gives a new proof of Goto's theorem.