Minimal displacement set for CAT(0) cubical complexes
Ioana-Claudia Lazar
TL;DR
This paper studies the minimal displacement set in CAT(0) cubical complexes, revealing its convexity, local CAT(0) structure, and simple connectivity, thus advancing understanding of their geometric properties.
Contribution
It establishes new structural properties of the minimal displacement set in CAT(0) cubical complexes, including convexity and local CAT(0) metric structure.
Findings
The minimal displacement set is convex.
It is locally endowed with a CAT(0) metric.
It is simply connected.
Abstract
We investigate the structure of the minimal displacement set in CAT(0) cubical complexes. We show that such set is convex, it is locally endowed with a CAT(0) metric and it is simply connected.
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Taxonomy
TopicsTopological and Geometric Data Analysis · Point processes and geometric inequalities · Homotopy and Cohomology in Algebraic Topology