论文标题
得出的微分流形
Derived Differentiable Manifolds
论文作者
论文摘要
我们根据弯曲的$ l_ \ infty [1] $ - 代数，即阳性振幅的DG歧管，发展了派生的差异几何理论。我们证明了派生的歧管的类别是原始对象的类别。因此，我们可以理解在派生的歧管同拷贝类别中平滑的歧管中亚法尔德的“同型纤维纤维产物”和“衍生的相交”。我们使用路径空间构建对角线的分解。首先，我们使用AKSZ构造动机的实际路径空间来构建无限的分解，然后使用Fiorenza-Manetti方法降低到有限维度。主要成分是弯曲$ l_ \ infty [1] $ - 代数的同型转移定理。 我们还证明了派生流形的逆函数定理，并研究了衍生流的弱等效性与准同构之间的关系。
We develop the theory of derived differential geometry in terms of bundles of curved $L_\infty[1]$-algebras, i.e. dg manifolds of positive amplitudes. We prove the category of derived manifolds is a category of fibrant objects. Therefore, we can make sense of "homotopy fibered product" and "derived intersection" of submaifolds in a smooth manifold in the homotopy category of derived manifolds. We construct a factorization of the diagonal using path spaces. First we construct an infinite-dimensional factorization using actual path spaces motivated by the AKSZ construction, then we cut down to finite dimensions using the Fiorenza-Manetti method. The main ingredient is the homotopy transfer theorem for curved $L_\infty[1]$-algebras. We also prove the inverse function theorem for derived manifolds, and investigate the relationship between weak equivalence and quasi-isomorphism for derived manifolds.
