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Publications [#287261] of Richard Hain
search www.ams.org.Papers Published
 Hain, RM, The Hodge De Rham theory of relative Malcev completion,
Annales Scientifiques De L’École Normale Supérieure, vol. 31 no. 1
(January, 1998),
pp. 4792 [pdf], [doi]
(last updated on 2019/05/25)
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.


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