Equivariant K-Theory and Refined Vafa–Witten Invariants

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