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.

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Sources & referencesView supporting material

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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