The Hodge De Rham theory of relative Malcev completion


Journal Article

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.

Full Text

Duke Authors

Cited Authors

  • Hain, RM

Published Date

  • January 2, 1998

Published In

Volume / Issue

  • 31 / 1

Start / End Page

  • 47 - 92

International Standard Serial Number (ISSN)

  • 0012-9593

Digital Object Identifier (DOI)

  • 10.1016/S0012-9593(98)80018-9

Citation Source

  • Scopus