Journal of the Mathematical Society of Japan

A note on bounded-cohomological dimension of discrete groups

Clara LÖH

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Bounded-cohomological dimension of groups is a relative of classical cohomological dimension, defined in terms of bounded cohomology with trivial coefficients instead of ordinary group cohomology. We will discuss constructions that lead to groups with infinite bounded-cohomological dimension, and we will provide new examples of groups with bounded-cohomological dimension equal to 0. In particular, we will prove that every group functorially embeds into an acyclic group with trivial bounded cohomology.

Article information

J. Math. Soc. Japan, Volume 69, Number 2 (2017), 715-734.

First available in Project Euclid: 20 April 2017

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Zentralblatt MATH identifier

Primary: 55N35: Other homology theories 20J06: Cohomology of groups 20E99: None of the above, but in this section

bounded cohomology cohomological dimension mitotic groups


LÖH, Clara. A note on bounded-cohomological dimension of discrete groups. J. Math. Soc. Japan 69 (2017), no. 2, 715--734. doi:10.2969/jmsj/06920715.

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