Witten's conjecture relating Donaldson and Seiberg–Witten invariants
Witten's conjecture relating Donaldson and Seiberg–Witten invariants
Let be a smooth, closed, oriented 4-manifold with and odd . Let have Seiberg–Witten simple type, and let be the Donaldson basic classes of , with corresponding nonzero Donaldson coefficients . A class is a Seiberg–Witten basic class when .
Witten's conjecture. Then has simple type; the basic classes of are precisely the Seiberg–Witten basic classes of ; and there is a nonzero constant depending only on such that
for all . This conjecture proposes a precise relationship between Donaldson and Seiberg–Witten invariants. The source introduces it after recalling the Donaldson structure theorem; no resolution status is supplied in the provided text.
Sources & referencesView supporting material
Primary source
John A. Baldwin and Steven Sivek, “Stein fillings and SU(2) representations”, arXiv:1611.05629 (2016).
Additional references
8 papers in this index state this conjecture (1995–2016). The statement above is taken from the most recent of them; the others are arXiv:1408.5085, arXiv:1408.5307, arXiv:math/0609530, arXiv:math/0106221, arXiv:math/9907107, arXiv:dg-ga/9509005, arXiv:alg-geom/9505018.
Progress summary
Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.
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