Borel asymptotic dimension of the Roller boundary of finite dimensional CAT(0) cube complexes
Koichi Oyakawa
TL;DR
This paper establishes that the Borel asymptotic dimension of the Roller boundary's median graph in finite dimensional CAT(0) cube complexes is bounded above by the complex's dimension, linking geometric and measure-theoretic properties.
Contribution
It proves a new upper bound on the Borel asymptotic dimension of the Roller boundary in finite dimensional CAT(0) cube complexes.
Findings
Borel asymptotic dimension is bounded by the complex's dimension.
The result applies to countable finite dimensional CAT(0) cube complexes.
Links geometric structure with measure-theoretic properties.
Abstract
We prove that for any countable finite dimensional CAT(0) cube complex, the Borel median graph on its Roller compactification has the Borel asymptotic dimension bounded from above by its dimension.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Mathematical Dynamics and Fractals · Geometric and Algebraic Topology