Michael Field.

Resolving actions of compact Lie groups

A general process for the desingularization of smooth actions of compact Lie groups is described. If G is a compact Lie group, it is shown that there is naturally associated to any compact G-manifold M, a compact G x (z/2)^p manifofd on which G acts monotypically. Here Z/2 denotes the cyclic group of order 2 and p + 1 is less than or equal to the number of orbit types for the action of G on M.

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