Asymptotic Dimension and Boundaries of Hyperbolic Spaces
Thanos Gentimis
TL;DR
This paper constructs an example of a hyperbolic space demonstrating that the asymptotic dimension can be strictly greater than the boundary dimension, highlighting a nuanced relationship between these geometric invariants.
Contribution
It provides a specific example of a hyperbolic space where the asymptotic dimension exceeds the boundary dimension, illustrating a new aspect of hyperbolic geometry.
Findings
Example of hyperbolic space with asdimX=2 and dim(bdry X)=0
Shows asymptotic dimension can be greater than boundary dimension in hyperbolic spaces
Highlights complexity in the relationship between space and boundary dimensions
Abstract
We give an example of a visual Gromov Hyperbolic metric space X with asdimX=2 and dim(bdry X)=0
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Taxonomy
TopicsGeometric and Algebraic Topology · Mathematical Dynamics and Fractals · Mathematics and Applications