On Donaldson and Seiberg-Witten invariants
Abstract
This article is based on a lecture by the first author at the International Georgia Topology Conference 2001 (Athens, Georgia) and the Mathematische Arbeitstagung 2001 (Bonn, Germany). We sketch a proof of Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree c+2, with c = -{1/4}(7 chi + 11 sigma), for four-manifolds obeying some mild conditions, where chi and sigma are their Euler characteristic and signature. We use the moduli space of SO(3) monopoles as a cobordism between a link of the Donaldson moduli space of anti-self-dual SO(3) connections and links of the moduli spaces of Seiberg-Witten monopoles. Gluing techniques allow us to compute contributions from Seiberg-Witten moduli spaces lying in the first (or `one-bubble') level of the Uhlenbeck compactification of the moduli space of SO(3) monopoles.
Cite
@article{arxiv.math/0106221,
title = {On Donaldson and Seiberg-Witten invariants},
author = {Paul M. N. Feehan and Thomas G. Leness},
journal= {arXiv preprint arXiv:math/0106221},
year = {2012}
}
Comments
Lecture notes for talk by the first author at the International Georgia Topology Conference 2001 (Athens, Georgia) and the Mathematische Arbeitstagung 2001 (Bonn, Germany). 11 pages