The de rham homotopy theory of complex algebraic varieties I

In this paper we use Chen's iterated integrals to put a mixed Hodge structure on the homotopy Lie algebra of an arbitrary complex algebraic variety, generalizing work of Deligne and Morgan. Similar techniques are used to put a mixed Hodge structure on other topological invariants associated with varieties that are accessible to rational homotopy theory such as the cohomology of the free loopspace of a simply connected variety.Supported in part by the National Science Foundation through grants MCS-8201642, DMS-8401175 and MCS-8108814(A04).