We construct Hodge filtered function spaces associated to infinite loop spaces. For Brown–Peterson cohomology, we show that the corresponding Hodge filtered spaces satisfy an analog of Wilson’s unstable splitting. As a consequence, we obtain an analog of Quillen’s theorem for Hodge filtered Brown–Peterson cohomology for complex manifolds.

中文翻译：

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Hodge中不稳定的分裂过滤了Brown-Peterson的同调

我们构造与无限循环空间相关的霍奇滤波函数空间。对于Brown–Peterson的同调，我们证明了对应的Hodge滤波空间满足Wilson的不稳定分裂的类比。结果，我们获得了复杂流形的霍奇滤波布朗-彼得森同调的奎伦定理的类似物。