|
|
|
Nankai Tracts in Mathematics - Vol. 7
ITERATED INTEGRALS AND CYCLES ON ALGEBRAIC MANIFOLDS
by Bruno Harris (Brown University, USA)
This subject has been of great interest both to topologists and to number theorists. The first part of this book describes some of the work of Kuo-Tsai Chen on iterated integrals and the fundamental group of a manifold. The author attempts to make his exposition accessible to beginning graduate students. He then proceeds to apply Chen's constructions to algebraic geometry, showing how this leads to some results on algebraic cycles and the Abel–Jacobi homomorphism. Finally, he presents a more general point of view relating Chen's integrals to a generalization of the concept of linking numbers, and ends up with a new invariant of homology classes in a projective algebraic manifold. The book is based on a course given by the author at the Nankai Institute of Mathematics in the fall of 2001.
Contents:
- Iterated Integrals, Chen's Flat Connection and p1
- Iterated Integrals on Compact Riemann Surfaces
- The Generalized Linking Pairing and the Heat Kernel
Readership: Researchers and graduate students in geometry and
topology.
“This book certainly is the first self contained introduction to this subject which is also adapted for non experts and graduate students.”
| 120pp |
Pub. date: Mar 2004 |
|
|
