arXiv subjects

Mateusz Kandybo

Publications and source records attributed to Mateusz Kandybo.

2 recordsLinked to original sources

arXiv2026

$E\mathcal{Z}$-boundaries, splittings over finite subgroups, and dense amalgams

The dense amalgam is an operation (introduced in arXiv:1410.4989) which to any finite collection of metrizable compacta associates canonically some new highly disconnected compact metrisable space in which embedded copies of the initial spaces are appropriately uniformly and disjointly distributed. We show that in the very general framework of $E\mathcal{Z}$-boundaries (unifying many frameworks such as Gromov boundaries, CAT(0)-boundaries, systolic boundaries, etc.), any boundary $Z$ of an infinitely ended group $Γ$ equipped with an appropriate splitting along finite subgroups has a form of the dense amalgam of the limit sets in $Z$ of the factor subgroups of this splitting.

math.GR↗

arXiv2025

On the biautomaticity of CAT(0) triangle-square groups

Following the research from the paper "Triangles, squares and geodesics" (arXiv:0910.5688) of Rena Levitt and Jon McCammond we investigate the properties of groups acting on CAT(0) triangle-square complexes, focusing mostly on biautomaticity of such groups. In particular we show two examples of nonpositively curved triangle-square complexes $X_1$ and $X_2$, such that their universal covers violate conjectures given in the aforementioned paper. This shows that the Gersten-Short geodesics cannot be used as a way of proving biautomaticity of groups acting on such complexes. Lastly we give a proof of biautomaticity of $π_1(X_1)$, however the biautomaticity of $π_1(X_2)$ remains unknown.

math.GR↗