The authors fix their Euclidean factor theorem for CAT(0) lattices: a lattice always commensurates a free abelian subgroup whose rank equals the Euclidean dimension, and finite generation or residual finiteness recovers the original splitting.
Commensurating HNN-extensions: non-positive curvature and biautomaticity
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abstract
We show that the commensurator of any quasiconvex abelian subgroup in a biautomatic group is small, in the sense that it has finite image in the abstract commensurator of the subgroup. Using this criterion we exhibit groups that are CAT(0) but not biautomatic. These groups also resolve a number of other questions concerning CAT(0) groups.
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2019 1verdicts
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Erratum and addenda to "Isometry groups of non-positively curved spaces: discrete subgroups"
The authors fix their Euclidean factor theorem for CAT(0) lattices: a lattice always commensurates a free abelian subgroup whose rank equals the Euclidean dimension, and finite generation or residual finiteness recovers the original splitting.