Contents

# Contents

## Idea

In group cohomology theory, if $G$ is a group which has torsion-free subgroups of finite index, then all such subgroups have the same cohomological dimension; this common dimension is called the virtual cohomological dimension of $G$ and denoted $vcd(G)$.

For example, $SL_n(\mathbb{Z})$ has infinite cohomological dimension, and yet

$vcd(SL_n(\mathbb{Z})) = \binom{n}{2}.$

notion of dimension

Last revised on March 21, 2021 at 03:30:41. See the history of this page for a list of all contributions to it.