Kavli Affiliate: Yukinobu Toda
| First 5 Authors: Tudor Pădurariu, Yukinobu Toda, , ,
| Summary:
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.
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