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Universal Embedding Spaces for Smooth G-Manifolds

For a compact Lie group G, a construction of a universal smooth G-manifold into which every n-dimensional smooth G-manifold embeds with trivial normal bundle, uniquely up to equivariant isotopy. The inverse limit of the cohomology of these universal spaces yields equivariant analogues of characteristic classes, and their cohomotopy groups are identified with equivariant bordism groups.