By Bruno Harris

This topic has been of serious curiosity either to topologists and to quantity theorists. the 1st a part of this publication describes many of the paintings of Kuo-Tsai Chen on iterated integrals and the elemental staff of a manifold. the writer makes an attempt to make his exposition obtainable to starting graduate scholars. He then proceeds to use Chen's structures to algebraic geometry, displaying how this ends up in a few effects on algebraic cycles and the Abel-Jacobi homomorphism. ultimately, he offers a extra normal perspective bearing on Chen's integrals to a generalization of the concept that of linking numbers, and finally ends up with a brand new invariant of homology periods in a projective algebraic manifold. The booklet is predicated on a path given by way of the writer on the Nankai Institute of arithmetic within the fall of 2001.

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