AMS Bookstore LOGO amslogo
Return to List

AMS TextbooksAMS Applications-related Books

Residues and Traces of Differential Forms via Hochschild Homology
Joseph Lipman
SEARCH THIS BOOK:

Contemporary Mathematics
1987; 95 pp; softcover
Volume: 61
ISBN-10: 0-8218-5070-9
ISBN-13: 978-0-8218-5070-1
List Price: US$26
Member Price: US$20.80
Order Code: CONM/61
[Add Item]

Request Permissions

Requiring only some understanding of homological algebra and commutative ring theory, this book will give those who have encountered Grothendieck residues in geometry or complex analysis a better understanding of residues, as well as an appreciation of Hochschild homology. While numerous papers have treated the topic of residues from a variety of viewpoints, no books have addressed this topic. The author fills this gap by using Hochschild homology to provide a natural, general, and easily accessible approach to residues, and by identifying connections with other treatments of residues. Developing a theory of the Grothendieck symbol by means of elementary homological and commutative algebra, the author derives residues from a simple pairing between Hochschild homology and cohomology groups, and defines all concepts along the way. The author also establishes some functorial properties and introduces certain trace and cotrace maps with potential use in other contexts.

Table of Contents

  • The residue homomorphism
  • Functorial properties
  • Quasi-regular sequences
  • Appendix A: Residues on algebraic varieties
  • Appendix B: Exterior differentiation
  • Trace and cotrace
Powered by MathJax

  AMS Home | Comments: webmaster@ams.org
© Copyright 2014, American Mathematical Society
Privacy Statement

AMS Social

AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia