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

Paul M.N. Feehan; Thomas G. Leness

doi:10.4171/jems/521

JournalsjemsVol. 17, No. 4pp. 899–923

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

Paul M.N. Feehan
Rutgers University, Piscataway, USA
Thomas G. Leness
Florida International University, Miami, USA

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Abstract

We prove that Witten's Conjecture [40] 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 $b_{2}^{+} \geq 3$ follows from our $SO (3)$ -monopole cobordism formula [6] when the four-manifold has $c_{1}^{2} \geq χ_{h} - 3$ or is abundant.

Cite this article

Paul M.N. Feehan, Thomas G. Leness, Witten's Conjecture for many four-manifolds of simple type. J. Eur. Math. Soc. 17 (2015), no. 4, pp. 899–923

DOI 10.4171/JEMS/521