Differential Geometry and Mathematical Physics pp 635-692 | Cite as

# The Gauge Orbit Space

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## Abstract

In the first part, we discuss the mathematical structure of the gauge orbit space stratification, including a Tubular Neighbourhood Theorem and a Regularity Theorem. Moreover, we show that every stratum admits a natural Riemannian metric, calculate its volume element and find the corresponding Riemann curvature. In the second part, we present our results on the enumeration of gauge orbit types for the gauge group \(G = \text {SU}(n)\) in detail. The classification is given in terms of certain characteristic classes fulfilling a number of algebraic relations. We also show how the natural partial ordering of strata can be read off from these relations.