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arXiv · 2409.10800

Topological K-theory of quasi-BPS categories for Higgs bundles

Tudor Pădurariu·Yukinobu Toda
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Abstract

In a previous paper, we introduced quasi-BPS categories for moduli stacks of semistable Higgs bundles. Under a certain condition on the rank, Euler characteristic, and weight, the quasi-BPS categories (called BPS in this case) are non-commutative analogues of Hitchin integrable systems. We proposed a conjectural equivalence between BPS categories which swaps Euler characteristics and weights. The conjecture is inspired by the Dolbeault Geometric Langlands equivalence of Donagi--Pantev, by the Hausel--Thaddeus mirror symmetry, and by the $χ$-independence phenomenon for BPS invariants of curves on Calabi-Yau threefolds. In this paper, we show that the above conjecture holds at the level of topological K-theories. When the rank and the Euler characteristic are coprime, such an isomorphism was proved by Groechenig--Shen. Along the way, we show that the topological K-theory of BPS categories is isomorphic to the BPS cohomology of the moduli of semistable Higgs bundles.

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Tudor Pădurariu, Yukinobu Toda. 2024-09-17. Topological K-theory of quasi-BPS categories for Higgs bundles. https://arxiv.org/abs/2409.10800

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