# Equivariant K-Theory and Refined Vafa–Witten Invariants

@article{Thomas2018EquivariantKA, title={Equivariant K-Theory and Refined Vafa–Witten Invariants}, author={Richard P. Thomas}, journal={arXiv: Algebraic Geometry}, year={2018} }

In [MT2] the Vafa-Witten theory of complex projective surfaces is lifted to oriented $\mathbb C^*$-equivariant cohomology theories. Here we study the K-theoretic refinement. It gives rational functions in $t^{1/2}$ invariant under $t^{1/2}\leftrightarrow t^{-1/2}$ which specialise to numerical Vafa-Witten invariants at $t=1$.
On the "instanton branch" the invariants give the virtual $\chi_{-t}^{}$-genus refinement of Gottsche-Kool. Applying modularity to their calculations gives predictions… Expand

#### 29 Citations

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