We introduce group actions on polyfolds and polyfold bundles. We prove quotient theorems for polyfolds, when the group action has finite isotropy. We prove that the sc-Fredholm property is preserved under quotient if the base polyfold is infinite dimensional. The quotient construction is the main technical tool in the construction of equivariant fundamental class in [42]. We also analyze the equivariant transversality near the fixed locus in the polyfold setting. In the case of $S^1$-action with fixed locus, we give a sufficient condition for the existence of equivariant transverse perturbations. We outline the application to Hamiltonian-Floer cohomology and a proof of the weak Arnold conjecture for general symplectic manifolds, assuming the existence of Hamiltonian-Floer cohomology polyfolds.

中文翻译：

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多重理论和S1等价横向性的商定理

我们介绍多折和多折束上的小组动作。当群作用具有有限的各向同性时，我们证明了多重折的商定理。我们证明，如果基多重折叠是无限维的，则在商数下保留了sc-Fredholm属性。商构造是[42]中等变基类构造的主要技术工具。我们还分析了多折叠设置中固定基因座附近的等变横向性。在具有固定轨迹的$ S ^ 1 $作用的情况下，我们给出了等变横向扰动存在的充分条件。假设存在Hamiltonian-Floer同调多重性，我们概述了在Hamiltonian-Floer同调上的应用以及对一般辛流形的弱Arnold猜想的证明。