We'll establish basic properties of generlized Hopf invariants. We start with the homology and cohomology of configuration spaces and the relationship between our approachh and Boardman-Steer invariants. We then apply loopspace machinery to show relate cohomology of configuration spaces to our homotopy functionals. We'll also compare with approaches of Sullivan and Hain. We'll end with a number of ideas for further work - the Hopf invariant one problem for formal spaces, analogues at characteristic p, "homotopy Jacobians" for varieties, and rational mapping space invariants. |