MILD AND TAME HOMOTOPY-THEORY

Extending recent results on R-local homotopy theory, we demonstrate that 'mild' r-reduced Hopf algebras up to homotopy over Z can be modeled by 'mild' r-reduced differential graded Lie algebras (DGL's) over Z. This equivalence can be applied to the Adams-Hilton model of a 1-connected CW complex, yielding a mild DGL model. We then show that this model induces an equivalence of the tame homotopy categories of spaces and DGL's, generalizing slightly the equivalence proved by Dwyer. The advantage of the new proof lies in the computability of the DGL model.