On higher order homological finiteness of rewriting systems

On higher order homological finiteness of rewriting systems Original Research Article 149-161 Stephen J. Pride, Friedrich Otto Close Close preview | Purchase PDF (229 K) | Related articles | Related reference work articles AbstractAbstract | Figures/TablesFigures/Tables | ReferencesReferences Abstract A sequence of finite rewriting systems image with the following properties is presented: (1) Rn is not of type FDT, (2) Rn is of type FHTn, but not of type FHTn+1, (3) Rn has word problem solvable in quadratic time.This result not only strengthens the result of Pride and Otto separating the geometric finiteness condition FDT from the finiteness condition FHT (=FHT1), but it also shows that the higher order homological finiteness conditions FHTn, which were first considered by McGlashan for dimension 2, yield an infinite hierarchy that is independent of the homotopical finiteness condition FDT. Article Outline 1. Introduction 2. The bi-augmentation ideal of a monoid 3. HNN-like extensions 4. Proof of Theorem 4 5. Proof of Theorem 5 6. Proof of main theorem References