Witten's conjecture for many four-manifolds of simple type

Abstract

We prove that Witten's Conjecture [arXiv:hep-th/9411102] on the relationship between the Donaldson and Seiberg-Witten series for a four-manifold of Seiberg-Witten simple type with $b_1=0$ and odd $b_2^{+}\ge 3$ follows from our $\mathrm{SO}(3)$-monopole cobordism formula [arXiv:math/0203047] when the four-manifold has $c_1^2\ge {\chi }_h-3$ or is abundant.

27 pages. To appear in the Journal of the European Mathematical Society. Incorporates final galley proof corrections corresponding to published version

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