nLab virtual cohomological dimension




In group cohomology theory, if GG 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 GG and denoted vcd(G)vcd(G).

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

vcd(SL n())=(n2). vcd(SL_n(\mathbb{Z})) = \binom{n}{2}.

notion of dimension

Last revised on March 21, 2021 at 07:30:41. See the history of this page for a list of all contributions to it.