PU(2) monopoles and links of top-level Seiberg-Witten moduli spaces
arXiv:math/0007190 · doi:10.1515/crll.2001.069
Abstract
This is the first of two articles in which we give a proof - for a broad class of four-manifolds - of Witten's conjecture that the Donaldson and Seiberg-Witten series coincide, at least through terms of degree less than or equal to c-2, where c is a linear combination of the Euler characteristic and signature of the four-manifold. This article is a revision of sections 1-3 of an earlier version of the article dg-ga/9712005, now split into two parts, while a revision of sections 4-7 of that earlier version appears in a recently updated dg-ga/9712005. In the present article, we construct virtual normal bundles for the Seiberg-Witten strata of the moduli space of PU(2) monopoles and compute their Chern classes.
Journal fur die Reine und Angewandte Mathematik, to appear; 64 pages
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- PU(2) monopoles. II: Top-level Seiberg-Witten moduli spaces and Witten's conjecture in low degrees
- PU(2) monopoles and a conjecture of Marino, Moore, and Peradze
- An SO(3)-version of 2-torsion instanton invariants
- Superconformal simple type and Witten's conjecture
- The SO(3) monopole cobordism and superconformal simple type
- What do Topologists want from Seiberg--Witten theory? (A review of four-dimensional topology for physicists)
- A vanishing result for a Casson-type instanton invariant
- Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds
- A Supersymmetric Quantum Field Theory Formulation of the Donaldson Polynomial Invariants
- The SO(3) Vortex Equations over Orbifold Riemann Surfaces