Non-abelian Seiberg-Witten theory and projectively stable pairs

Abstract

We introduce the concept of Spin^G-structure in a SO-bundle, where $G\subset U(V)$ is a compact Lie group containing $-i{d}_V$. We study and classify $Spi{n}^G(4)$-structures on 4-manifolds, we introduce the G-Monopole equations associated with a $Spi{n}^G$-structure. On Kaehler surfaces a Kobayashi-Hitchin correspondence can be proved for the corresponding moduli spaces. Using this complex geometric interpretation, we determine explicitely a moduli space of "PU(2)-Monopoles" on ${\P }^2$, we describe its Uhlenbeck compactification, as well as the Donaldson- and the abelian locus.

TeX-Type: LaTeX, 31 pages, revised version

References in corpus (1)

• Quaternionic Monopoles

Cited by in corpus (7)

• PU(2) monopoles and relations between four-manifold invariants
• Duality in Topological Quantum Field Theories
• Topological correlators of $SU(2)$, $\mathcal{N}=2^{\ast }$ SYM on four-manifolds
• Generalised monopole equations on Kahler surfaces
• Duality in the Context of Topological Quantum Field Theory
• Duality and Topological Quantum Field Theory
• Virtual Morse-Bott index, moduli spaces of pairs, and applications to topology of smooth four-manifolds