Traces of Differential Forms and Hochschild Homology

1989
ISBN: 978-3-540-50985-1
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1368, 118 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 201 g

Reihe: Lecture Notes in Mathematics

This monograph provides an introduction to, as well as a unification and extension of the published work and some unpublished ideas of J. Lipman and E. Kunz about traces of differential forms and their relations to duality theory for projective morphisms.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

Zielgruppe

Research

Autoren/Hrsg.

Hübl, Reinhold

Fachgebiete

• Mathematik | Informatik Mathematik Geometrie Differentialgeometrie
• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Topologie Algebraische Topologie

Inhaltsverzeichnis

The Hochschild homology and the Hochschild cohomology of a topological algebra.- Differential forms and Hochschild homology.- Traces in Hochschild homology.- Traces of Differential Forms.- Traces in complete intersections.- The topological residue homomorphism.- Trace formulas for residues of differential forms.