English

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 c+2c+2, with c=1/4(7χ+11σ)c=-{1/4}(7\chi+11\sigma), for four-manifolds obeying some mild conditions, where χ\chi and σ\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.

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