Hidden symmetry of the K-theoretic Pandharipande–Thomas series

Prove that, after analytic continuation in q, a suitable identification of equivariant variables, and possibly a restriction of curve-class variables, the K-theoretic Pandharipande–Thomas series is independent of the choice of one-dimensional subtorus G_m,q⊂T used to define the threefold fixed locus.

Background

The Gromov–Witten series depends only on the full torus action and not on the auxiliary choice of a one-dimensional subtorus used to define the Pandharipande–Thomas theory. The conjectured correspondence therefore predicts a corresponding symmetry on the sheaf-theoretic side.

The paper verifies this symmetry in selected local-curve and local-projective examples.