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Brahim Abdenbi

Publications and source records attributed to Brahim Abdenbi.

4 recordsLinked to original sources
arXiv2024

The Hrushovski Property for Compact Special Cube Complexes

We show that any compact nonpositively curved cube complex $Y$ embeds in a compact nonpositively curved cube complex $R$ where each combinatorial injective partial local isometry of $Y$ extends to an automorphism of $R$. When $Y$ is special and the collection of injective partial local isometries satisfies certain conditions, we show that $R$ can be chosen to be special and the embedding $Y\hookrightarrow R$ can be chosen to be a local isometry.

math.GN↗
arXiv2023

Negative Immersions and Finite Height Mappings

Given a monomorphism $Ψ:\mathcal{H}\rightarrow \mathcal{F}$ where $\mathcal{H}$ is a proper free factor of the free group $\mathcal{F}$, we show the associated mapping torus $X$ of $Ψ$ has negative immersions iff $\mathcal{H}$ has finite height in $π_1X$ iff $Ψ$ is fully irreducible. We survey related properties and discuss possible directions to pursue further.

math.GR↗
arXiv2023

On Unique Factorization of Non-periodic Words

Given a bi-order $\succ$ on the free group $\mathcal{F}$, we show that every non-periodic cyclically reduced word $W\in \mathcal{F}$ admits a maximal ascent that is uniquely positioned. This provides a cyclic permutation of $W'$ that decomposes as $W'=AD$ where $A$ is the maximal ascent and $D$ is either trivial or a descent. We show that if $D$ is not uniquely positioned in $W$, then it must be an internal subword in $A$. Moreover, we show that when $\succ$ is the Magnus ordering, $D=1_\mathcal{F}$ if and only if $W$ is monotonic.

math.CO↗