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- Title
Periodic flat resolutions and periodicity in group (co)homology.
- Authors
Asadollahi, Javad; Hajizamani, Ali; Salarian, Shokrollah
- 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 after some steps with the periodicity isomorphisms of homology groups induced by the cap product with an element in , where is the cotorsion envelope of the trivial -module , if and only if it has periodic cohomology of period after some steps with the periodicity isomorphisms of cohomology groups induced by the cup product with an element in .
- Subjects
HOMOLOGY theory; ALGEBRAIC topology; ISOMORPHISM (Mathematics); MODULES (Algebra); FREE resolutions (Algebra); GROUP theory
- Publication
Forum Mathematicum, 2012, Vol 24, Issue 2, p273
- ISSN
0933-7741
- Publication type
Article
- DOI
10.1515/form.2011.060