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Traces of Differential Forms and Hochschild Homology

  • Book
  • © 1989

Overview

Authors:
  1. Reinhold Hübl
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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
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  2. Introduction

    • Reinhold Hübl
    Pages 1-7

  3. The Hochschild homology and the Hochschild cohomology of a topological algebra

    • Reinhold Hübl
    Pages 8-27

  4. Differential forms and Hochschild homology

    • Reinhold Hübl
    Pages 28-46

  5. Traces in Hochschild homology

    • Reinhold Hübl
    Pages 47-55

  6. Traces of Differential Forms

    • Reinhold Hübl
    Pages 56-69

  7. Traces in complete intersections

    • Reinhold Hübl
    Pages 70-83

  8. The topological residue homomorphism

    • Reinhold Hübl
    Pages 84-93

  9. Trace formulas for residues of differential forms

    • Reinhold Hübl
    Pages 94-105

  10. Back Matter

    Pages 106-111
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Keywords

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This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms.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.

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

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