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arXiv · 2405.14850

Floer-theoretic filtration on Painlev\'e Hitchin systems

Szilárd Szabó·Filip Živanović
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Abstract

We classify equivariant $\mathbb{C}^*$-actions on moduli spaces of Higgs bundles corresponding to the Painlev\'e equations. Using this, we compute the Floer-theoretic filtrations on the cohomology of these spaces, introduced by Ritter and the second author in arXiv:2304.13026. We compare it with the ``$P=W$'' and the filtration obtained by multiplicities of the irreducible components of the nilpotent cone, ultimately deducing that the Floer-theoretic filtration coincides with the multiplicity filtration, for all 2-dimensional Higgs moduli.

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Szilárd Szabó, Filip Živanović. 2024-05-23. Floer-theoretic filtration on Painlev\'e Hitchin systems. https://arxiv.org/abs/2405.14850

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