3 papers
math.GR2025
The conjecture for affine Artin groups
Giovanni Paolini, Mario Salvetti
In this summary paper, we present the key ideas behind the recent proof of the conjecture for affine Artin groups, which states that complements of locally finite affine…
math.LO2025
First-order aspects of Artin groups
Alberto Cassella, Gianluca Paolini, Giovanni Paolini
We prove several results on the model theory of Artin groups, focusing on Artin groups which are ``far from right-angled Artin groups''. The first result is that if i…
math.GR2025
Dual structures on Coxeter and Artin groups of rank three
Emanuele Delucchi, Giovanni Paolini, Mario Salvetti
We extend the theory of dual Coxeter and Artin groups to all rank-three Coxeter systems, beyond the previously studied spherical and affine cases. Using geometric, combinatorial, a…