# Good Wild Harmonic Bundles and Good Filtered Higgs Bundles

## TL;DR

This paper establishes a correspondence between good wild harmonic bundles and filtered flat bundles, providing new insights into their structure and potential applications in constructing Frobenius manifolds.

## Contribution

It proves the Kobayashi-Hitchin correspondence for good wild harmonic bundles and filtered $
abla$-flat bundles, extending the theory to cases with group action homogeneity.

## Key findings

- Established the Kobayashi-Hitchin correspondence for good wild harmonic bundles.
- Analyzed the correspondence in the presence of group action homogeneity.
- Suggested a new approach to constructing Frobenius manifolds.

## Abstract

We prove the Kobayashi-Hitchin correspondence between good wild harmonic bundles and polystable good filtered $\lambda$-flat bundles satisfying a vanishing condition. We also study the correspondence for good wild harmonic bundles with the homogeneity with respect to a group action, which is expected to provide another way to construct Frobenius manifolds.