# 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}
}
• Richard P. Thomas
• Published 28 September 2018
• Mathematics, Physics
• arXiv: Algebraic Geometry
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
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