论文标题
弯曲L-侵入空间的逆函数定理
The inverse function theorem for curved L-infinity spaces
论文作者
论文摘要
在本文中，我们证明了衍生微分几何形状中的逆函数定理。更具体地说，我们表明弯曲的$ l_ \ infty $空间的形态是一种准i晶状体，在某种程度上是局部同型逆逆向。该定理同时概括了平滑歧管的逆函数定理和$ l_ \ infty $代数的Whitehead定理。主要成分是$ l_ \ infty $同构的阻塞理论（在弯曲的环境中）和弯曲$ l_ \ l_ \ infty $代数的同型转移定理。这两种技术在$ a_ \ infty $ case中也有效。
In this paper we prove an inverse function theorem in derived differential geometry. More concretely, we show that a morphism of curved $L_\infty$ spaces which is a quasi-isomorphism at a point has a local homotopy inverse. This theorem simultaneously generalizes the inverse function theorem for smooth manifolds and the Whitehead theorem for $L_\infty$ algebras. The main ingredients are the obstruction theory for $L_\infty$ homomorphisms (in the curved setting) and the homotopy transfer theorem for curved $L_\infty$ algebras. Both techniques work in the $A_\infty$ case as well.
