11 papers
Undecidability of the Diophantine problem for one-relator groups and one-relation monoids
Carl-Fredrik Nyberg-Brodda
We prove that the Diophantine problem, i.e. the problem of solving equations with coefficients, in one-relator groups and one-relation monoids is undecidable in general. Specifical…
Braid groups are not profinitely rigid
Carl-Fredrik Nyberg-Brodda
We show that the -strand braid group is not profinitely rigid when . We do this by exhibiting a family of pairwise non-isomorphic, finitely presented re…
On homological finiteness properties and free inverse monoids
Carl-Fredrik Nyberg-Brodda
We construct a simple and useful sufficient condition, based on actions on a lattice of idempotents, for monoids admitting homomorphisms to the monogenic free inverse monoid $\math…
The Baumslag-Gersten group and a problem of Olshanskii
Carl-Fredrik Nyberg-Brodda
We prove that a certain representation of the Baumslag-Gersten one-relator group by germs of continuous functions is not faithful. This gives a negative answer t…
On profinite rigidity, Grothendieck pairs, and the second homology of some -orbifold groups
Carl-Fredrik Nyberg-Brodda
The second homology group is of central importance in the study of profinite rigidity of -manifold groups. Although general and deep results imply that the integral homology of…
A note on right-angled Artin subgroups of one-relator groups
Carl-Fredrik Nyberg-Brodda
We give a short proof of the following result due to Howie: if is a right-angled Artin group embedding into some one-relator group, then is a finite forest. The proof…