Universal-formula conjecture for lower-level PU(2) monopole pairings

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Let ℓ\ell, FF, L1L_1, s0\mathfrak{s}_0, SW(s0⊗L1)SW(\mathfrak{s}_0\otimes L_1), and QXQ_X denote the level, bundle and line-bundle data, Seiberg–Witten invariant, and intersection form appearing in the Pidstrigach–Tyurin reduction formula. Universal-formula conjecture. The pairing on the right-hand side of that reduction formula is given by a universal formula depending only on ℓ\ell, FF, L1L_1, SW(s0⊗L1)SW(\mathfrak{s}_0\otimes L_1), the intersection form QXQ_X, and invariants of the homotopy type of XX. Such a formula would provide the universal Seiberg–Witten-theoretic input needed to turn the reduction formula into a relation between Donaldson and Seiberg–Witten invariants; the source presents this as an important step toward proving Witten's conjecture.

References

Primary source

Paul M. N. Feehan and Thomas G. Leness, “PU(2) monopoles and relations between four-manifold invariants”, arXiv:dg-ga/9709022 (1997).

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