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September 10, 2025AxiomsOpen Access

Injective Hulls of Infinite Totally Split-Decomposable Metric Spaces

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The study investigates the structure of injective hulls in infinite totally split-decomposable metric spaces, suggesting they share properties with CAT(0) cube complexes.
Key results include the characterization of injective hulls and the generalization of previous decomposition theories, enhancing our understanding of metric space structures.
Utilizing innovative approaches, the research provides necessary conditions for proper actions on CAT(0) cube complexes, specifically related to groups with word metrics.
The findings reveal that injective hulls of odd cycles yield cell complexes isomorphic to CAT(0) cube complexes, highlighting significant applications in geometry.

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This analysis connects injective hulls and CAT(0) cube complexes in totally split-decomposable metric spaces, indicating new structural insights.

Maël Pavón (2025) studied this question.

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This analysis connects injective hulls and CAT(0) cube complexes in totally split-decomposable metric spaces, indicating new structural insights.