Borel asymptotic dimension of the Roller boundary of finite dimensional
 CAT(0) cube complexes

Q: What type of study is this?

This is a Quantitative Study study.

Koichi Oyakawa

doi:10.48550/arxiv.2505.10334

May 15, 2025Open Access

Borel asymptotic dimension of the Roller boundary of finite dimensional CAT(0) cube complexes

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Key Points

Borel asymptotic dimension is shown to be bounded from above by the dimension in these complexes.
The study highlights the relationship between the structure of finite dimensional CAT(0) cube complexes and their Borel median graphs.
The Roller compactification provides a significant framework in understanding these dimensions in the context of geometry.
This finding suggests that Borel asymptotic dimension behaves predictively in the context of cube complexes.

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Implication

Theorem proves Borel asymptotic dimension is bounded by dimension in finite dimensional CAT(0) cube complexes.

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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Cite This Study

Koichi Oyakawa (2025) studied this question.

synapsesocial.com/papers/68f163c79903599108abcb03 https://doi.org/10.48550/arxiv.2505.10334

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Borel asymptotic dimension of the Roller boundary of finite dimensional CAT(0) cube complexes

Key Points

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Implication

Abstract

Discussion

Cite This Study

Borel asymptotic dimension of the Roller boundary of finite dimensional CAT(0) cube complexes

Key Points

Ask about this paper

Implication

Abstract

Discussion

Cite This Study

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