Publications [#287261] of Richard Hain

Papers Published

1. Hain, RM, The Hodge De Rham theory of relative Malcev completion, Annales Scientifiques de l'Ecole Normale Superieure, vol. 31 no. 1 (1998), pp. 47-92 [pdf], [doi]
   (last updated on 2025/04/05)

   Abstract:
   Suppose that X is a smooth manifold and ρ : π1 (X,N) → S is a representation of the fundamental group of X into a real reductive group with Zariski dense image. To such data one can associate the Malcev completion G of π1(X,x) relative to ρ. In this paper we generalize Chen's iterated integrals and show that the H0 of a suitable complex of these iterated integrals is the coordinate ring of G. This is used to show that if X is a complex algebraic manifold and ρ is the monodromy representation of a variation of Hodge structure over X, then the coordinate ring of G has a canonical mixed Hodge structure. © Elsevier, Paris.