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  • © 1989

Traces of Differential Forms and Hochschild Homology

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Part of the book series: Lecture Notes in Mathematics (LNM, volume 1368)

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Table of contents (8 chapters)

  1. Front Matter

    Pages I-III
  2. Introduction

    • Reinhold Hübl
    Pages 1-7
  3. Differential forms and Hochschild homology

    • Reinhold Hübl
    Pages 28-46
  4. Traces in Hochschild homology

    • Reinhold Hübl
    Pages 47-55
  5. Traces of Differential Forms

    • Reinhold Hübl
    Pages 56-69
  6. Traces in complete intersections

    • Reinhold Hübl
    Pages 70-83
  7. The topological residue homomorphism

    • Reinhold Hübl
    Pages 84-93
  8. Back Matter

    Pages 106-111

About this book

This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms. The approach uses Hochschild-homology, the definition of which is extended to the category of topological algebras. Many results for Hochschild-homology of commutative algebras also hold for Hochschild-homology of topological algebras. In particular, after introducing an appropriate notion of completion of differential algebras, one gets a natural transformation between differential forms and Hochschild-homology of topological algebras. Traces of differential forms are of interest to everyone working with duality theory and residue symbols. Hochschild-homology is a useful tool in many areas of k-theory. The treatment is fairly elementary and requires only little knowledge in commutative algebra and algebraic geometry.

Keywords

  • K-theory
  • algebraic geometry
  • cohomology
  • homology
  • residue

Bibliographic Information

  • Book Title: Traces of Differential Forms and Hochschild Homology

  • Authors: Reinhold Hübl

  • Series Title: Lecture Notes in Mathematics

  • DOI: https://doi.org/10.1007/BFb0098406

  • Publisher: Springer Berlin, Heidelberg

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer-Verlag Berlin Heidelberg 1989

  • Softcover ISBN: 978-3-540-50985-1Published: 22 March 1989

  • eBook ISBN: 978-3-540-46125-8Published: 08 December 2006

  • Series ISSN: 0075-8434

  • Series E-ISSN: 1617-9692

  • Edition Number: 1

  • Number of Pages: VI, 118

  • Topics: Algebraic Geometry, Analysis

Buying options

eBook USD 29.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 39.95
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions