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virtual cohomological dimension

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Idea

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}.

Last revised on March 24, 2019 at 14:13:01. See the history of this page for a list of all contributions to it.