Moduli spaces of noncommutative instantons: gauging away noncommutative parameters

Abstract

Using the theory of noncommutative geometry in a braided monoidal category, we improve upon a previous construction of noncommutative families of instantons of arbitrary charge on the deformed sphere S^4_θ. We formulate a notion of noncommutative parameter spaces for families of instantons and we explore what it means for such families to be gauge equivalent, as well as showing how to remove gauge parameters using a noncommutative quotient construction. Although the parameter spaces are a priori noncommutative, we show that one may always recover a classical parameter space by making an appropriate choice of gauge transformation.

v2: 44 pages; minor changes. To appear in Quart. J. Math

References in corpus (1)

• Families of Monads and Instantons from a Noncommutative ADHM Construction

Cited by in corpus (10)

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• Mapping spaces and automorphism groups of toric noncommutative spaces
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• On the Relationship between Classical and Deformed Hopf Fibrations
• The Noncommutative Topology of Anti-Self-Dual Gauge Fields