Mathematicians are human, so we make mistakes. However, whether the result one wants to cite contains an error is often very hard to decide, without having to dive into the arguments. Hence I thought I'll keep here a list of published papers in Geometric Group Theory which contain an incorrect statement or proof. The list is work in progress and by no mean complete, so if you want to add an entry please send me an email.
Automorphisms and abstract commensurators of 2-dimensional Artin groups
Issue: Given an amalgamated free product of two Artin groups A and B along a common parabolic C, and an element g centralising C, the author defines a Dehn Twist automorphism as the map that conjugates A by g and fixes B. This is a well-defined endomorphism, but it might fail to be an isomorphism if G does not lie in either A or B. There are already counterexamples in free groups.
Solution: Unknown to me, though I expect all Dehn Twists appearing in Crisp's paper are by elements in one of the factors. I'd be grateful if someone pointed out a clean solution.
Largest acylindrical actions and stability in hierarchically hyperbolic groups
Carolyn Abbott, Jason Behrstock, Daniel Berlyne, Matthew Gentry Durham, Jacob Russell
Issue: Remark A.7 from the Appendix claims that an almost HHG structure on a group can be competed to a genuine HHG structure. However, the action on the new domain set might not be cofinite, as the construction from the proof of Theorem A.1 adds a domain for every container pair.
Solution: An almost HHG structure can be completed to a G-HHS structure, that is, a HHS structure with a geometric action of a group.
Extra-large type Artin groups are hierarchically hyperbolic
Issue: Lemma 4.4 claims that, given a \(\mathbb{Z}\)-central extension of a hyperbolic group and a family of cyclic subgroups whose projections are independent, there exists a homogeneous quasimorphism which is unbounded on \(\mathbb{Z}\) and trivial on the given cyclic subgroups. This is already false in the Klein bottle group.
Solution: Remark A.5 from this paper of mine shows that the error does not affect the results of Hagen, Martin, and Sisto. This is because the above Lemma can be replaced by Corollary A.4 from the same article, which further requires the cyclic directions to be central in their normalisers.