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arXiv · 2302.04346

On the stabilization of the topological complexity of graph braid groups

Ben Knudsen
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Abstract

We establish a strong, geometric lower bound on the (sequential) topological complexity of the unordered configuration spaces of a general graph. As an application, we show that, for most graphs, the topological complexity eventually stabilizes at its maximal possible value, a direct analogue of a stability phenomenon in the ordered setting first conjectured by Farber. We estimate the stable range in terms of the number of trivalent vertices.

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Ben Knudsen. 2023-02-08. On the stabilization of the topological complexity of graph braid groups. https://arxiv.org/abs/2302.04346

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