7 problems

Non-biautomaticity conjecture. The group $\Gamma$ is not biautomatic.

Let $X_2$ be the specific compact locally CAT(0) triangle-square complex constructed in the paper. Biautomaticity conjecture for $X_2$. The fundamental group $\pi_1(X_2)$ is biauto…

Let $X$ be a compact locally CAT(0) triangle-square complex such that no intrinsically aperiodic flat embeds in $\widetilde{X}$ and there are only finitely many distinct thoroughly…

Let $X$ be a compact locally CAT(0) triangle-square complex. A flat is thoroughly crumpled if it is crumpled and there is a bound on the number of cells in each region. Levitt–McCa…

Let $X$ be a compact locally CAT(0) triangle-square complex, and let $F$ be an intrinsically aperiodic flat, meaning that $F$ does not admit a cocompact cellular action of…

Let $K$ be a compact nonpositively curved triangle-square complex, and let a thoroughly crumpled plane mean the type of flat plane defined in the source. Thoroughly crumpled planes…

Let $K$ be a compact nonpositively curved triangle-square complex, meaning a complex built from triangles and squares with nonpositive curvature, and let $\pi_1(K)$ denote its fund…