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Groups with infinite homology

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Cohomological Methods in Homotopy Theory

Part of the book series: Progress in Mathematics ((PM,volume 196))

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Abstract

We consider the reduced homology of a group G with coefficients in the trivial module:

$$\widetilde H(G) = \mathop \oplus \limits_{n = 1}^\infty {H_n}(G;\mathbb{Z}).$$

A group is said to be acyclic if its reduced homology vanishes. Many interesting classes of groups have been discovered having this property ([2] is a useful survey). This is an indication that the reduced homology carries limited information.

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Author information

Authors and Affiliations

  1. Department of Mathematics, National University of Singapore, Kent Ridge 117543, Singapore

    A. J. Berrick

  2. School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, London, El 4NS, UK

    P. H. Kropholler

Authors
  1. A. J. Berrick
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  2. P. H. Kropholler
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Editor information

Editors and Affiliations

  1. Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193, Bellaterra, Spain

    Jaume Aguadé , Carles Broto  & Carles Casacuberta ,  & 

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© 2001 Springer Basel AG

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Berrick, A.J., Kropholler, P.H. (2001). Groups with infinite homology. In: Aguadé, J., Broto, C., Casacuberta, C. (eds) Cohomological Methods in Homotopy Theory. Progress in Mathematics, vol 196. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8312-2_4

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  • DOI: https://doi.org/10.1007/978-3-0348-8312-2_4

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9513-2

  • Online ISBN: 978-3-0348-8312-2

  • eBook Packages: Springer Book Archive

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