Moore–Witten conjecture for SU(2) Donaldson invariants of CP^2

Consider the complex projective plane CP2\mathbb{C}\mathrm{P}^2 with gauge group SU(2)\mathrm{SU}(2). Its regularized uu-plane integral has a contribution from the cusp at τ=\tau=\infty. Moore–Witten conjecture for CP2\mathbb{C}\mathrm{P}^2. The contribution from the cusp at τ=\tau=\infty to the regularized uu-plane integral of CP2\mathbb{C}\mathrm{P}^2 for the gauge group SU(2)\mathrm{SU}(2) is equal to the generating function for the SU(2)\mathrm{SU}(2)-Donaldson invariants of CP2\mathbb{C}\mathrm{P}^2. The source explicitly identifies this as the remaining open case of the broader Moore–Witten conjecture.

Sources & referencesView supporting material

Primary source

Andreas Malmendier, “Donaldson invariants of CP^1 x CP^1 and Mock Theta Functions”, arXiv:1008.0175 (2011).

Additional references

2 papers in this index state this conjecture (2008–2010). The statement above is taken from the most recent of them; the others are arXiv:0808.1442.

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