Skip to main content

Spectral sequences. Abelian groups

  • Chapter
Strong Shape and Homology

Part of the book series: Springer Monographs in Mathematics ((SMM))

  • 691 Accesses

Abstract

The proof of the key result of the next section (Theorem 21.6) uses in an essential way the Roos spectral sequence and its consequences, which we describe in this section (see 20.3). In order to make the text as self-contained as possible, we develop general techniques of spectral sequences in subsections 20.1 and 20.2. In 20.4 we discuss pure extensions of abelian groups and in 20.5 we establish the needed results from the theory of abelian groups.

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

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • Godement, R. (1958): Topologie algébrique et théorie des faisceaux. Hermann, Paris

    MATH  Google Scholar 

  • Mardesié, S., Prasolov, A.V. (1988): Strong homology is not additive. Trans. Amer. Math. Soc. 307, 725–744

    MathSciNet  Google Scholar 

  • Mardesié, S., Prasolov, A.V. (1998): On strong homology of compact spaces. Topology Appl. 82, 327–354

    Article  MathSciNet  Google Scholar 

  • Roos, J.- E. (1961): Sur les foncteurs dérivés de lim. Applications. C. R. Acad. Sci. Paris 252, 3702–3704

    MathSciNet  MATH  Google Scholar 

  • Gruson, L., Jensen, C.U. (1981): Dimension cohomologiques reliées aux fonc- teurs lim(’), in Séminaire d’algèbre Paul Dubreil et Marie-Paule Malliavin. Proc. Paris 1980, Lecture Notes in Math. 867, Springer, Berlin Heidelberg New York, pp. 234–294

    Google Scholar 

  • Jensen, C.U. (1972): Les foncteurs dérivés de lim et leurs applications enthéorie des modules. Lecture Notes in Math. 254, Springer, Berlin Heidelberg New York

    Google Scholar 

  • Jensen, C.U. (1977): On the global dimension for the functor category (mod R, Ab). J. Pure Appl. Algebra 11, 45–51

    Article  MathSciNet  Google Scholar 

  • Kuz’minov, V. (1967): On derived functors of the projective limit functor. Sibirski Mat. Z. 8, No. 2, 333–345

    MathSciNet  MATH  Google Scholar 

  • Kuz’minov, V. (1971): Derived functors of inverse limits and extension classes. Sibirski Mat. Z. 12, No. 2, 384–396

    MathSciNet  MATH  Google Scholar 

  • Kuz’minov, V., Shvedov, I.A. (1974): Covering spectra in the theory of cohomology and homology of topological spaces. Sibirski Mat. Z. 15, 1083–1102

    MATH  Google Scholar 

  • Kuz’minov, V., Shvedov, I.A. (1975): Hyperhomology of limits of direct spectra of complexes and homology groups of topological spaces. Sibirski Mat. Z. 16, 49–59

    Article  MATH  Google Scholar 

  • Huber, M., Meier, W. (1978): Cohomology theories and infinite CW-complexes. Comment. Math. Helv. 53, 239–257

    Article  MathSciNet  MATH  Google Scholar 

  • Huber, P. (1961): Homotopy theories in general categories. Math. Ann. 444, 361–385

    Article  Google Scholar 

  • Nöbeling, G. (1961): Uber die derivierten des inversen and des direkten Limes einer Modul-Familie. Topology 1, 47–61

    Article  Google Scholar 

  • Nöbeling, G. (1968): Verallgemeinerung eines Satzes von Herrn E. Specker. Inventiones Math. 6, 41–55

    Article  MATH  Google Scholar 

  • Fuchs, L. (1970): Infinite abelian groups, Vol. I. Academic Press, New York

    MATH  Google Scholar 

  • Kaplansky, I. (1954): Infinite abelian groups, Univ. Michigan Press, Ann Arbor

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Mardešić, S. (2000). Spectral sequences. Abelian groups. In: Strong Shape and Homology. Springer Monographs in Mathematics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-13064-3_21

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-13064-3_21

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-08546-8

  • Online ISBN: 978-3-662-13064-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics