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

Paul M. N. Feehan; Thomas G. Leness

doi:10.4171/JEMS/521

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

Differential Geometry 2016-04-08 v5 Mathematical Physics Algebraic Geometry Geometric Topology math.MP

Authors: Paul M. N. Feehan , Thomas G. Leness

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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 $b_2^+\geq 3$ follows from our $\mathrm{SO}(3)$ -monopole cobordism formula [arXiv:math/0203047] when the four-manifold has $c_1^2\geq \chi_h-3$ or is abundant.

Keywords

witten conjecture donaldson series seiberg-witten series four-manifold so(3)-monopole cobordism simple type

Cite

@article{arxiv.math/0609530,
  title  = {Witten's conjecture for many four-manifolds of simple type},
  author = {Paul M. N. Feehan and Thomas G. Leness},
  journal= {arXiv preprint arXiv:math/0609530},
  year   = {2016}
}

Comments

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

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

Abstract

Keywords

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