Download or read book Iterated Integrals and Cycles on Algebraic Manifolds written by Bruno Harris and published by World Scientific. This book was released on 2004 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This subject has been of great interest both to topologists and tonumber theorists. The first part of this book describes some of thework of Kuo-Tsai Chen on iterated integrals and the fundamental groupof a manifold. The author attempts to make his exposition accessibleto beginning graduate students. He then proceeds to apply Chen''sconstructions to algebraic geometry, showing how this leads to someresults on algebraic cycles and the AbelOCoJacobihomomorphism. Finally, he presents a more general point of viewrelating Chen''s integrals to a generalization of the concept oflinking numbers, and ends up with a new invariant of homology classesin a projective algebraic manifold. The book is based on a coursegiven by the author at the Nankai Institute of Mathematics in the fallof 2001."