Abstract
Abstract Let G be a compact Lie group. Previously (Section 2.8) the term G-vector bundle meant a vector bundle with group G as the structure group. It has another accepted meaning (used throughout the remainder of this text) when G acts on the base space of the vector bundle. In this case there are two groups to deal with, G and the structure group of the bundle. We shall deal exclusively with the structure groups SO(2) and SO(3). In this context, a G-vector bundle is a vector bundle (of dimension 2 or 3) with G acting to preserve the inner product and orientation, commuting with base projection, and mapping fibres directly to fibres (see [1]).
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