Traces of Differential Forms and Hochschild Homology
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"Traces of Differential Forms and Hochschild Homology" by Reinhold Hübl is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms.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.
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"Traces of Differential Forms and Hochschild Homology" by Reinhold Hübl is a mathematics book and learning resource focused on Core Mathematics. Best for teachers, students, and readers looking for stronger mathematical understanding.
Topic: Core Mathematics
Author: Reinhold Hübl
Who this is for:
- Teachers and classroom instructors
- Students building subject mastery
- Readers looking for practical learning support
Why this book matters: It stands out as a practical math resource that helps explain concepts, strengthen problem-solving, and support classroom or independent learning.
This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms.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.
| Author | Reinhold Hübl |
| Publisher | Lecture Notes in Mathematics |
| Published | 1989-03-22 |
| ISBN-13 | 9783540509851 |
| Binding | Paperback |
| Pages | 136 |
| Language | English |
| Subjects | Mathematics |
| Topic | Core Mathematics |
| Series | Lecture Notes in Mathematics |
Format: Paperback
Length: 136 pages
Language: English
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