Iterated integrals and cycles on algebraic manifolds / Bruno Harris.

Format:

Book

Author/Creator:

Harris, Bruno.

Contributor:

Chen, K.-T. (Kuo-Tsai), 1923-1987.

Series:

Nankai tracts in mathematics ; v. 7.

Nankai tracts in mathematics ; v. 7

Language:

English

Subjects (All):

Integrals.

Algebraic cycles.

Algebraic number theory.

Manifolds (Mathematics).

Geometry, Algebraic.

Physical Description:

1 online resource (121 p.)

Edition:

1st ed.

Place of Publication:

Singapore ; River Edge, NJ : World Scientific, c2004.

Language Note:

English

Summary:

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 Abel-Jacobihomomorphism. Finally, he presents a more general point of viewrelating Chen's integrals to a generalization of the concept oflinking numbers, and ends

Contents:

Interated Integrals and Cycles on Algebraic Manifolds; Preface; Contents; 1. Iterated Integrals, Chen's Flat Connection and 1; 2. Iterated Integrals on Compact Riemann Surfaces; 3. The Generalized Linking Pairing and the Heat Kernel; Appendix: Orientations, Fiber Integration; Bibliography; List of Notations; Index

Notes:

"Part of this book describes some of the work of Kuo-Tsai Chen on iterated integrals and the fundamental group of a manifold ... Based on a course by the author at the Nankai Institute of Mathematics in the fall of 2001."

Includes bibliographical references (p. 101-102) and index.

ISBN:

9786611872502

9781281872500

1281872504

9789812562579

9812562575

OCLC:

475937386