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

From papers

Let \ell, FF, L1L_1, s0\mathfrak{s}_0, SW(s0L1)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 \ell, FF, L1L_1, SW(s0L1)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.

Progress summary

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Sources & referencesView supporting material

Primary source

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

Solutions 0

No solutions have been posted yet.