滤子L-无穷代数的Goldman-Millson定理
A Version of the Goldman-Millson Theorem for Filtered L-infinity Algebras
摘要：
本文研究了具有完全降滤子的$L_{\infty}$ -代数.证明了在较弱的条件下，$L_{\infty}$拟同构$U: L \to \tilde{L}$诱导了分别对应于$L$和$\tilde{L}$的Deligne-Getzler-Hinich（DGH）$\infty$ -广群之间的弱等价性.本文可以被认为是对Ezra Getzler的基础论文arXiv：math/0404003的适度补充。
英文摘要：
In this paper we consider $L_{\infty}$-algebras equipped with complete descending filtrations. We prove that, under some mild conditions, an $L_{\infty}$ quasi-isomorphism $U: L \to \tilde{L}$ induces a weak equivalence between the Deligne-Getzler-Hinich (DGH) $\infty$-groupoids corresponding to $L$ and $\tilde{L}$, respectively. This paper may be considered as a modest addition to foundational paper arXiv:math/0404003 by Ezra Getzler.
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