Iterated Integrals and Algebraic Cycles: Examples and Prospects

Details Iterated Integrals and Algebraic Cycles: Examples and Prospects Iterated Integrals and Algebraic Cycles: Examples and Prospects

2001-09-25

arxiv.org/abs/math/0109204v2

Mathematics

Algebraic Geometry

45 pages, Latex 2e, 3 eps figures. There are several minor corrections and stylistic changes. One figure is corrected

Scientific paper

This paper is for the proceedings of the Chen-Chow Conference held in Tianjin, China in October 2000. The goal of the paper is to produce and survey evidence for a connection between Chen's work on iterated integrals on the one hand, and algebraic cycles and motives on the other. The paper is expository, and begins with an introduction to Chen's work. Topics covered include loop space de Rham theorems; iterated integrals of currents; the works of Carlson-Clemmens-Morgan and Bruno Harris on periods of mixed Hodge structures on homotopy groups and algebraic cycles; the cobar construction, algebraic loopspace de Rham Theorems; and generalized iterated integrals.

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