A relation between the total instanton number and the quantum-numbers of magnetic monopoles that arise in general Abelian gauges in SU(2) YangMills theory is established. The instanton number is expressed as the sum of the ‘twists’ of all monopoles, where the twist is related to a generalized Hopf invariant. The origin of a stronger relation between instantons and monopoles in the Polyakov gaug...

The terminology and notation used in this paper are introduced in the following articles: [20], [25], [2], [7], [18], [21], [8], [3], [4], [16], [13], [23], [14], [17], [5], [11], [12], [1], [19], [6], [10], [15], [22], [24], and [9]. We adopt the following convention: C denotes a simple closed curve, i, j, n denote natural numbers, and p denotes a point of E T . The following propositions are ...

This is a brief overview of some applications of the ideas of abstract convexity to the upper semilattices of gauges in finite dimensions.