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Proper topological complexity

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This work characterizes topological complexity in configuration spaces, suggesting implications for homotopy invariants.

Proper topological complexity provides insight into how algorithms navigate configuration spaces without entering unsafe areas.
The study identifies proper topological complexity as a homotopy functorial invariant related to exterior sectional category.
By analyzing exterior maps, we relate this concept to the broader framework of exterior homotopy categories.
This framework enhances understanding of algorithmic motion within mathematical topology.

García-Calcines et al. (2025) studied this question.

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