Simple Search

Query:

Enter a query and click »Search«...

Format:

Display: entries per page entries

Zbl 0911.14008
Hain, Richard M.
The Hodge de Rham theory of relative Malcev completion. (English)
[J] Ann. Sci. Éc. Norm. Supér. (4) 31, No. 1, 47-92 (1998). ISSN 0012-9593

Suppose that $X$ is a smooth manifold and $\rho: \pi_1 (X,x)\to S$ 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 ${\cal G}$ of $\pi_1(X,x)$ relative to $\rho$. In this paper Chen's iterated integrals are generalized and it is shown that the $H^0$ of a suitable complex of these iterated integrals is the coordinate ring of ${\cal G}$. This is used to show that if $X$ is a complex algebraic manifold and $\rho$ is the monodromy representation of a variation of Hodge structure over $X$, then the coordinate ring of ${\cal G}$ has a canonical mixed Hodge structure.
[M.Teicher (Ramat Gan)]

MSC 2000:: *14F35 Homotopy theory (algebraic geometry)
14D07 Variation of Hodge structures
57M05 Fundamental group, etc.

Keywords: fundamental group; variation of Hodge structure

Comment on this Item PDF MathML XML ASCII DVI PS BibTeX Online Ordering Article Article Article Journal Journal Journal

	Scientific prize winners of the ICM 2010
	Overhang
	Lie groups, physics and geometry. An introduction for physicists, engineers and chemists.

Simple Search

Zentralblatt MATH Berlin [Germany]