Mochizuki's formula with partition-function coefficients

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Let XX be a smooth 44-manifold with b1=0b_1=0 and odd b+≥3b_+\geq 3. Let βi\beta_i, KiK_i, β(τ)\beta(\tau), ρ(τ)\rho(\tau), β(τ)⊥\beta(\tau)^{\perp}, τ\tau, ξ~1\tilde\xi_1, ξ~2\tilde\xi_2, ξ~3\tilde\xi_3, ξ~4\tilde\xi_4, yy, aa, ξ1\xi_1, and ξ\xi denote the quantities occurring in Mochizuki's result, Theorem~, and the partition formula, Theorem~; let A~(ξ1,y;a)\widetilde{\mathcal A}(\xi_1,y;a) and B(ξ1,ξ;a)\mathcal B(\xi_1,\xi;a) be the corresponding expressions.

Mochizuki's conjecture. Mochizuki's result holds for XX, up to sign, when A~(ξ1,y;a)\widetilde{\mathcal A}(\xi_1,y;a) is replaced by the coefficients of B(ξ1,ξ;a)\mathcal B(\xi_1,\xi;a) in the partition formula.

This is the paper's proposed relation between Mochizuki's formula and the partition-function expression for Donaldson invariants. The supplied text gives no resolution status, and the precise coefficient extraction and notation depend on results stated elsewhere in the paper.

References

Primary source

Lothar Göttsche, Hiraku Nakajima and Kota Yoshioka, “Donaldson = Seiberg-Witten from Mochizuki's formula and instanton counting”, arXiv:1001.5024 (2010).

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