## Journal of the Mathematical Society of Japan

### A note on bounded-cohomological dimension of discrete groups

Clara LÖH

#### Abstract

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

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

Dates
First available in Project Euclid: 20 April 2017

https://projecteuclid.org/euclid.jmsj/1492653644

Digital Object Identifier
doi:10.2969/jmsj/06920715

Mathematical Reviews number (MathSciNet)
MR3638282

Zentralblatt MATH identifier
1376.55005

#### Citation

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. https://projecteuclid.org/euclid.jmsj/1492653644

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