6 papers
The word problem for two-generator one-relator inverse monoids
Robert D. Gray, Catherine Reilly
We study the word problem in two-generator one-relator inverse monoids, proving both decidability and undecidability results. We give the first example of a two-generator one-relat…
The Diophantine problem in the Baumslag-Gersten group
Robert D. Gray, Alex Levine
We show that, for every positive prime number , the Baumslag-Gersten group has an undecidable Diophantine pro…
Finite complete rewriting systems for graphs of free groups with applications to free-by-cyclic, one-relator, and three-manifold groups
Robert D. Gray, Marco Linton
We prove that any finite graph of finitely generated free groups admits a finite complete rewriting system after possibly taking a free product with a free group of rank two. As a…
Undecidable Diophantine problems in generalisations of one-relator groups
Robert D. Gray, Alex Levine
Motivated by the open problem of whether all one-relator groups have decidable Diophantine problem, in this paper we prove a collection of undecidability results about the Diophant…
Membership problems in braid groups and Artin groups
Robert D. Gray, Carl-Fredrik Nyberg-Brodda
We study several natural decision problems in braid groups and Artin groups. We classify the Artin groups with decidable submonoid membership problem in terms of the non-existence…
Magnus submonoids and membership problems in one-relator, surface and hyperbolic groups
Islam Foniqi, Robert D. Gray
Motivated by its applications to the word problem for one-relator inverse monoids, via results of Ivanov, Margolis, and Meakin (2001), we prove several decidability and undecidabil…