Maurer-Cartan模与Riemann-Hilbert型定理
Maurer-Cartan moduli and theorems of Riemann-Hilbert type
摘要：
我们研究Maurer-Cartan模空间的dg代数和相关的dg类别，并表明，而不是拟同构不变量，他们是不变量的强同伦型，一个自然的概念，还没有研究过。我们证明，在几个不同的情况下，Schlessinger-Stasheff型定理比较的概念同伦和规范等价的Maurer-Cartan元素，以及它们的categorized版本。作为应用，我们重新证明和推广了Block-Smith的高阶Riemann-Hilbert对应，并将其推广到单纯复形和拓扑空间.
英文摘要：
We study Maurer-Cartan moduli spaces of dg algebras and associated dg categories and show that, while not quasi-isomorphism invariants, they are invariants of strong homotopy type, a natural notion that has not been studied before. We prove, in several different contexts, Schlessinger-Stasheff type theorems comparing the notions of homotopy and gauge equivalence for Maurer-Cartan elements as well as their categorified versions. As an application, we re-prove and generalize Block-Smith's higher Riemann-Hilbert correspondence, and develop its analogue for simplicial complexes and topological spaces.
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