  We introduce a new integral invariant for isometric actions of compact Lie
groups, the copolarity. Roughly speaking, it measures how far from being polar
the action is. We generalize some results about polar actions in this context.
In particular, we develop some of the structural theory of copolarity k
representations, we classify the irreducible representations of copolarity one,
and we relate the copolarity of an isometric action to the concept of
variational completeness in the sense of Bott and Samelson.
