SO(3) Monopoles, Level-One Seiberg-Witten Moduli Spaces, and Witten's Conjecture in Low Degrees
Differential Geometry
2016-04-08 v2 High Energy Physics - Theory
Mathematical Physics
Geometric Topology
math.MP
Abstract
We prove Witten's formula relating the Donaldson and Seiberg-Witten series modulo powers of degree , with , for four-manifolds obeying some mild conditions, where and 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.
Keywords
Cite
@article{arxiv.math/0106238,
title = {SO(3) Monopoles, Level-One Seiberg-Witten Moduli Spaces, and Witten's Conjecture in Low Degrees},
author = {Paul M. N. Feehan and Thomas G. Leness},
journal= {arXiv preprint arXiv:math/0106238},
year = {2016}
}
Comments
Minor corrections; details added. Topology and its Applications, 91 pages, to appear