Homology, Homotopy and Applications

Cohomology of groups with operators

A. M. Cegarra, J. M. García-Calcines, and J. A. Ortega

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Abstract

Well-known techniques from homological algebra and algebraic topology allow one to construct a cohomology theory for groups on which the action of a fixed group is given. After a brief discussion on the modules to be considered as coefficients, the first section of this paper is devoted to providing some definitions for this cohomology theory and then to proving that they are all equivalent. The second section is mainly dedicated to summarizing certain properties of this equivariant group cohomology and to showing several relationships with the ordinary group cohomology theory.

Article information

Source
Homology Homotopy Appl., Volume 4, Number 1 (2002), 1-23.

Dates
First available in Project Euclid: 13 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.hha/1139840051

Mathematical Reviews number (MathSciNet)
MR1894065

Zentralblatt MATH identifier
1007.18013

Subjects
Primary: 20J06: Cohomology of groups
Secondary: 18G10: Resolutions; derived functors [See also 13D02, 16E05, 18E25] 55N25: Homology with local coefficients, equivariant cohomology

Citation

Cegarra, A. M.; García-Calcines, J. M.; Ortega, J. A. Cohomology of groups with operators. Homology Homotopy Appl. 4 (2002), no. 1, 1--23. https://projecteuclid.org/euclid.hha/1139840051


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