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28 March 2024
 
  » arxiv » math.DG/0106238

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SO(3) Monopoles, Level-One Seiberg-Witten Moduli Spaces, and Witten's Conjecture in Low Degrees
Paul M. N. Feehan ; Thomas G. Leness ;
Date 27 Jun 2001
Subject Differential Geometry; Mathematical Physics; Geometric Topology | math.DG hep-th math-ph math.GT math.MP
AbstractWe prove Witten’s formula relating the Donaldson and Seiberg-Witten series modulo powers of degree $c+2$, with $c=-{1/4}(7chi+11sigma)$, 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.
Source arXiv, math.DG/0106238
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