Skip to main content

Variations on Cyclic Homology

  • Chapter
Cyclic Homology

Part of the book series: Grundlehren der mathematischen Wissenschaften ((GL,volume 301))

  • 541 Accesses


There are several ways of modifying cyclic homology: by altering the cyclic bicomplex, by putting up other groups than the cyclic groups or by enlarging the category of algebras.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

USD 9.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliographical Comments on Chapter 5

  • Avramov, L., Halperin, S., On the vanishing of cotangent cohomology, Comment. Math. Helv. 62 (1987), 169–184.

    Article  MathSciNet  MATH  Google Scholar 

  • Block, J.L., Cyclic homology of filtered algebras, K-theory 1 (1987), 515–518.

    Article  MathSciNet  MATH  Google Scholar 

  • Block, J.L., Cyclic homology of filtered algebras, K-theory 1 (1987), 515–518.

    Google Scholar 

  • Brown, R., Loday, J.-L., Van Kampen theorems for diagrams of spaces, Topology 26 (1987), 311–335

    Article  MathSciNet  MATH  Google Scholar 

  • Krasauskas, R.L., Skew simplicial groups, Litovsk. Mat. Sb. 27 (1987) No. 1, 89–99

    MathSciNet  Google Scholar 

  • Lodder, J.M., Dihedral homology and the free loop space, Proc. London Math. Soc. 60 (1990), 201–224.

    MATH  Google Scholar 

  • Dunn, G., Dihedral and quaternionic homology and mapping spaces, K-theory 3 (1989), 141–161.

    Article  MathSciNet  MATH  Google Scholar 

  • Wolters, P., Generalized Arf invariants and reduced power operations in cyclic homology, thesis, Nijmegen, 1990.

    Google Scholar 

  • ViguÉ-Poirrier, M., Burghelea, D., A model for cyclic homology and algebraic K-theory of 1-connected topological spaces, J. Diff. Geom. 22 (1985), 243–253.

    Google Scholar 

  • Goodwillie, T.G., Relative algebraic K-theory and cyclic homology, Ann. Of Math. 124 (1986), 347–402. 88b: 18008

    Google Scholar 

  • Brylinski, J.-L., Getzler, E., The homology of algebras of pseudo-differential symbols and the non-commutative residue, K-theory 1 (1987), 385–403

    Article  MathSciNet  MATH  Google Scholar 

  • Geller, S., Reid, L., Weibel, C., The cyclic homology and K-theory of curves, J. Reine Ang. Math. 393 (1989), 39–90

    MathSciNet  MATH  Google Scholar 

  • Feigin, B.L., Tsygan, B.L., Cyclic homology of algebras with quadratic relations, universal enveloping algebras and group algebras, in “K-theory, Arithmetic and Geometry”, Springer Lect. Notes in Math. 1289 (1987), 210–239

    Article  MathSciNet  Google Scholar 

  • Kassel, C., Cyclic homology, comodules and mixed complexes, J. of Algebra 107 (1987), 195–216.

    Article  MathSciNet  MATH  Google Scholar 

  • Dwyer, W.G., Kan, D.M., Normalizing the cyclic modules of Connes, Comment. Math. Helv. 60 (1985) 582–600.

    Article  MathSciNet  MATH  Google Scholar 

  • Connes, A., Gromov, M., Moscovici, H. Conjectures de Novikov et fibrés presque plats, C. R. Acad. Sci. Paris Sér. A-B 310 (1990), 273–277. 91e: 57041

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations


Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Loday, JL. (1992). Variations on Cyclic Homology. In: Cyclic Homology. Grundlehren der mathematischen Wissenschaften, vol 301. Springer, Berlin, Heidelberg.

Download citation

  • DOI:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-21741-2

  • Online ISBN: 978-3-662-21739-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics