TY - JOUR AB - For any free oriented Borel–Moore homology theory A, we construct an associative product on the A-theory of the stack of Higgs torsion sheaves over a projective curve C. We show that the resulting algebra AHa0C admits a natural shuffle presentation, and prove it is faithful when A is replaced with usual Borel–Moore homology groups. We also introduce moduli spaces of stable triples, heavily inspired by Nakajima quiver varieties, whose A-theory admits an AHa0C-action. These triples can be interpreted as certain sheaves on PC(ωC⊕OC). In particular, we obtain an action of AHa0C on the cohomology of Hilbert schemes of points on T∗C. AU - Minets, Sasha ID - 7683 IS - 2 JF - Selecta Mathematica, New Series SN - 10221824 TI - Cohomological Hall algebras for Higgs torsion sheaves, moduli of triples and sheaves on surfaces VL - 26 ER -