论文标题
平滑构造同拷贝的作用
Smooth constructions of homotopy-coherent actions
论文作者
论文摘要
我们证明，对于精美的无限维平滑基团G，平滑拓扑中的自然结构和符号拓扑中的G均产生了G的同型相干群体。这会产生无限二维平滑基团与同型均匀理论之间的桥梁。 结果依赖于两个计算：一个表明Milnor分类BG的差异同源群自然等于（连续）同型组，第二个表明特定的严格类别本地化以产生BG的同型类型。 然后，我们证明了符合性几何形状的结果：这些方法适用于liouville部门的liouville自动形态。目前的工作是针对[OT19]的，我们的构造表明，较高的同型自动形态群体的较高同型组映射到福卡亚类别类别不变性，我们在这里证明了来自2014 ICM的Teleman在liouville和Monotone设置中的猜想。
We prove that, for nice classes of infinite-dimensional smooth groups G, natural constructions in smooth topology and symplectic topology yield homotopically coherent group actions of G. This yields a bridge between infinite-dimensional smooth groups and homotopy theory. The result relies on two computations: One showing that the diffeological homotopy groups of the Milnor classifying space BG are naturally equivalent to the (continuous) homotopy groups, and a second showing that a particular strict category localizes to yield the homotopy type of BG. We then prove a result in symplectic geometry: These methods are applicable to the group of Liouville automorphisms of a Liouville sector. The present work is written with an eye toward [OT19], where our constructions show that higher homotopy groups of symplectic automorphism groups map to Fukaya-categorical invariants, and where we prove a conjecture of Teleman from the 2014 ICM in the Liouville and monotone settings.
