标题： 准BPS范畴的拓扑K理论对于Higgs丛 显示英文标题

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

摘要： 在之前的一篇论文中，我们为半稳定Higgs丛的模堆栈引入了准BPS范畴。 在秩、欧拉示性数和权满足一定条件的情况下，准BPS范畴（在这种情况下称为BPS）是Hitchin可积系统的非交换类比。 我们提出了一个关于BPS范畴的猜想等价关系，该关系交换欧拉示性数和权。 该猜想受到Donagi--Pantev的Dolbeault几何朗兰兹等价、Hausel--Thaddeus镜像对称以及Calabi-Yau三复流形上曲线的$\chi$不变现象对BPS不变量的启发。 在本文中，我们证明了上述猜想在拓扑K理论层面成立。 当秩和欧拉示性数互质时，这种同构由Groechenig--Shen证明。 在此过程中，我们证明了BPS范畴的拓扑K理论与半稳定Higgs丛模空间的BPS上同调同构。 显示英文摘要

摘要： 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 $\chi$-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.