Unstable splittings in Hodge filtered Brown-Peterson cohomology

TL;DR

This paper constructs Hodge filtered function spaces linked to Brown-Peterson cohomology, demonstrating an unstable splitting and an analog of Quillen's theorem, advancing the understanding of Hodge filtered cohomology in complex manifolds.

Contribution

It introduces Hodge filtered function spaces for Brown-Peterson cohomology and proves an unstable splitting and Quillen-type theorem in this context.

Findings

Hodge filtered spaces satisfy an unstable splitting similar to Wilson's.

An analog of Quillen's theorem is established for Hodge filtered Brown-Peterson cohomology.

Provides new tools for studying cohomology in complex geometry.

Abstract

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.