By Bruno Harris
This topic has been of serious curiosity either to topologists and to quantity theorists. the 1st a part of this booklet describes a number of the paintings of Kuo-Tsai Chen on iterated integrals and the basic crew of a manifold. the writer makes an attempt to make his exposition available to starting graduate scholars. He then proceeds to use Chen's buildings to algebraic geometry, exhibiting how this ends up in a few effects on algebraic cycles and the Abel-Jacobi homomorphism. ultimately, he offers a extra normal standpoint pertaining to Chen's integrals to a generalization of the idea that of linking numbers, and finally ends up with a brand new invariant of homology sessions in a projective algebraic manifold. The ebook relies on a direction given via the writer on the Nankai Institute of arithmetic within the fall of 2001.
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