Journal article
For rewriting systems the topological finiteness conditions FDT and FHT are not equivalent
Publication Details
Authors: | Pride, S.; Otto, F. |
Publication year: | 2004 |
Journal: | The Journal of the London Mathematical Society |
Pages range : | 363-382 |
Volume number: | 69 |
Abstract
A finite rewriting system is presented that does not satisfy the homotopical finiteness condition FDT, although it satisfies the homological finiteness condition FHT. This system is obtained from a group G and a finitely generated subgroup H of G through a monoid extension that is almost all HNN extension. The FHT property of the extension is closely related to the FP2 property for the subgroup H, while the FDT property of the extension is related to the finite presentability of H. The example system separating the FDT property from the FHT property is then obtained by applying this construction to an example group.
A finite rewriting system is presented that does not satisfy the homotopical finiteness condition FDT, although it satisfies the homological finiteness condition FHT. This system is obtained from a group G and a finitely generated subgroup H of G through a monoid extension that is almost all HNN extension. The FHT property of the extension is closely related to the FP2 property for the subgroup H, while the FDT property of the extension is related to the finite presentability of H. The example system separating the FDT property from the FHT property is then obtained by applying this construction to an example group.
