Undecidability of the word problem for one-relator inverse monoids via right-angled Artin subgroups of one-relator groups

Abstract: We prove the following results: (1) There is a one-relator inverse monoid $\mathrm{Inv}\langle A:|:w=1 \rangle$ with undecidable word problem; and (2) There are one-relator groups with undecidable submonoid membership problem. The first of these results answers a problem originally posed by Margolis, Meakin and Stephen in 1987.