Startseite Mathematik Periodic flat resolutions and periodicity in group (co)homology
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Periodic flat resolutions and periodicity in group (co)homology

  • Javad Asadollahi EMAIL logo , Ali Hajizamani und Shokrollah Salarian
Veröffentlicht/Copyright: 25. Februar 2012
Forum Mathematicum
Aus der Zeitschrift Band 24 Heft 2

Abstract.

Using the notion of flat covers and proper flat resolutions, we study modules with periodic flat resolutions. It follows that, equivalently, we may study modules with periodic homology. We specialize our results to the category of modules over integral group ring , where is an arbitrary group. Among other results, we show that if a group is in a certain class of groups, then has periodic homology of period q after some steps with the periodicity isomorphisms of homology groups induced by the cap product with an element in Hq(,C), where C is the cotorsion envelope of the trivial -module , if and only if it has periodic cohomology of period q after some steps with the periodicity isomorphisms of cohomology groups induced by the cup product with an element in Hq(,).

Keywords.: Proper resolution; periodic flat resolution; homology of groups
Received: 2009-12-05
Revised: 2010-03-31
Published Online: 2012-02-25
Published in Print: 2012-March

© 2012 by Walter de Gruyter Berlin Boston

Artikel in diesem Heft

  1. Masthead
  2. Uniform weighted estimates for oscillatory singular integrals
  3. Solutions of the linear Boltzmann equation and some Dirichlet series
  4. Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
  5. Periodic flat resolutions and periodicity in group (co)homology
  6. Precompact noncompact reflexive Abelian groups
  7. Free profinite p-rings
  8. Cellular covers for R-modules and varieties of groups
  9. Time changes of local Dirichlet spaces by energy measures of harmonic functions
  10. A construction of a universal connection
  11. Finitely generated algebraic structures with various divisibility conditions
  12. Quasiprojective varieties admitting Zariski dense entire holomorphic curves
  13. Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
https://doi.org/10.1515/form.2011.060
Schlagwörter für diesen Artikel
Proper resolution; periodic flat resolution; homology of groups

Artikel in diesem Heft

  1. Masthead
  2. Uniform weighted estimates for oscillatory singular integrals
  3. Solutions of the linear Boltzmann equation and some Dirichlet series
  4. Confluence and combinatorics in finitely generated unital lattice-ordered abelian groups
  5. Periodic flat resolutions and periodicity in group (co)homology
  6. Precompact noncompact reflexive Abelian groups
  7. Free profinite p-rings
  8. Cellular covers for R-modules and varieties of groups
  9. Time changes of local Dirichlet spaces by energy measures of harmonic functions
  10. A construction of a universal connection
  11. Finitely generated algebraic structures with various divisibility conditions
  12. Quasiprojective varieties admitting Zariski dense entire holomorphic curves
  13. Conservativeness of non-symmetric diffusion processes generated by perturbed divergence forms
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Heruntergeladen am 4.2.2026 von https://www.degruyterbrill.com/document/doi/10.1515/form.2011.060/pdf?lang=de
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