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Residues and Traces of Differential Forms via Hochschild Homology
 
Front Cover for Residues and Traces of Differential Forms via Hochschild Homology
Available Formats:
Electronic ISBN: 978-0-8218-7651-0
Product Code: CONM/61.E
List Price: $28.00
MAA Member Price: $25.20
AMS Member Price: $22.40
Front Cover for Residues and Traces of Differential Forms via Hochschild Homology
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Residues and Traces of Differential Forms via Hochschild Homology
Available Formats:
Electronic ISBN:  978-0-8218-7651-0
Product Code:  CONM/61.E
List Price: $28.00
MAA Member Price: $25.20
AMS Member Price: $22.40
  • Book Details
     
     
    Contemporary Mathematics
    Volume: 611987; 95 pp
    MSC: Primary 14; Secondary 13; 16; 32;

    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
     
     
    • Chapters
    • Introduction
    • 1 The residue homomorphism
    • 2 Functorial properties
    • 3 Quasi-regular sequences
    • 4 Trace and cotrace
    • References
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Volume: 611987; 95 pp
MSC: Primary 14; Secondary 13; 16; 32;

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.

  • Chapters
  • Introduction
  • 1 The residue homomorphism
  • 2 Functorial properties
  • 3 Quasi-regular sequences
  • 4 Trace and cotrace
  • References
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