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arXiv · 1811.10383

A Symbolic coding of the Morse boundary

Abdalrazzaq Zalloum
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Abstract

Let $X$ be a proper geodesic metric space. We give a new construction of the Morse Boundary that realizes its points as equivalence classes of functions on $X$ which behave similar to the "distance to a point" function. When $G=\langle S \rangle $ is a finitely generated group and $X=Cay(G,S)$, we use this construction to give a symbolic presentation of the Morse boundary as a space of "derivatives" on $Cay(G,S).$ The collection of such derivatives naturally embeds in the shift space $\mathcal{A}^G$ for some finite set $\mathcal{A}.$

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Abdalrazzaq Zalloum. 2018-11-26. A Symbolic coding of the Morse boundary. https://arxiv.org/abs/1811.10383

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