Finiteness Conditions

  • Kenneth S. Brown
Part of the Graduate Texts in Mathematics book series (GTM, volume 87)


Recall that the definition of H * (G, M) and H*(G, M) allows us to choose an arbitrary projective resolution P = (Pi)i0 of ℤ over ℤG. Similarly, if we wish to take the topological point of view, then we can compute H * (G, M) and H*(G, M) in terms of an arbitrary K(G, 1)-complex Y. Since we have this freedom of choice, it is reasonable to try to choose P (or Y) to be as “small” as possible, and this leads to various finiteness conditions on G.


Exact Sequence Finite Type Finite Index Duality Group Finite Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag New York Inc. 1982

Authors and Affiliations

  • Kenneth S. Brown
    • 1
  1. 1.Department of MathematicsCornell UniversityIthacaUSA

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