P. Przytycki

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math.GR2025

353-combinatorial curvature and the $3$ -dimensional $K (I ¨ , 1)$ conjecture

Jingyin Huang, Piotr Przytycki

We prove the $K (I ¨ , 1)$ conjecture for Artin groups of dimension $3$ . As an ingredient, we introduce a new form of combinatorial non-positive curvature.

math.GR2024

Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded

Anne Lonjou, Piotr Przytycki, Christian Urech

We prove that any finitely generated subgroup of the plane Cremona group consisting only of algebraic elements is of bounded degree. This follows from a more general result on `dec…

math.GR2024

Weak Tits alternative for groups acting geometrically on buildings

Chris Karpinski, Damian Osajda, Piotr Przytycki

We show that if a group $G$ acts geometrically by type-preserving automorphisms on a building, then $G$ satisfies the weak Tits alternative, namely, that $G$ is either virtually ab…

353-combinatorial curvature and the 3-dimensional K(I¨,1) conjecture

Finitely generated subgroups of algebraic elements of plane Cremona groups are bounded

Weak Tits alternative for groups acting geometrically on buildings

353-combinatorial curvature and the $3$ -dimensional $K (I ¨ , 1)$ conjecture