article epub_ahead yes Michael Groechenig author Shiyu Shen author 544cccd3-9005-11ec-87bc-94aef1c5b8140000-0002-4444-8718 TaHa department IST-BRIDGE: International postdoctoral program project We establish an isomorphism of complex K-theory of the moduli space M of “SL n​ ”-Higgs bundles of degree d and rank n (in the sense of Hausel–Thaddeus) and twisted complex K-theory of the orbifold M of PGL n​ -Higgs bundles of degree e, where (n,d)=(n,e)=1. Along the way, we prove the vanishing of torsion for H ∗ ( M ) and certain twisted complex K-theory groups of M . We also extend Arinkin’s autoduality of compactified Jacobian to a derived equivalence between SL n​ - and PGL n​ -Hitchin systems over the elliptic locus. In the appendix, we develop a formalism of G-sheaves of spectra, generalising equivariant homotopy theory to a relative setting. EMS Press2025 eng 1435-9855 1435-9863 2212.10695 00160825480000110.4171/jems/1601 Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. <a href="https://doi.org/10.4171/jems/1601">https://doi.org/10.4171/jems/1601</a>. M. Groechenig and S. Shen, “Complex K-theory of moduli spaces of Higgs bundles,” <i>Journal of the European Mathematical Society</i>. EMS Press, 2025. Groechenig M, Shen S. Complex K-theory of moduli spaces of Higgs bundles. <i>Journal of the European Mathematical Society</i>. 2025. doi:<a href="https://doi.org/10.4171/jems/1601">10.4171/jems/1601</a> Groechenig, M., &#38; Shen, S. (2025). Complex K-theory of moduli spaces of Higgs bundles. <i>Journal of the European Mathematical Society</i>. EMS Press. <a href="https://doi.org/10.4171/jems/1601">https://doi.org/10.4171/jems/1601</a> M. Groechenig, S. Shen, Journal of the European Mathematical Society (2025). Groechenig, Michael, and Shiyu Shen. “Complex K-Theory of Moduli Spaces of Higgs Bundles.” <i>Journal of the European Mathematical Society</i>, EMS Press, 2025, doi:<a href="https://doi.org/10.4171/jems/1601">10.4171/jems/1601</a>. Groechenig M, Shen S. 2025. Complex K-theory of moduli spaces of Higgs bundles. Journal of the European Mathematical Society. 200432025-07-21T07:54:50Z2026-07-23T11:16:00Z