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arXiv · 2510.00201

Representation asymptotics in the homology of pure graph braid groups

Louis Hainaut·Ben Knudsen·Nicholas Wawrykow
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Abstract

We give explicit formulas for the asymptotic Betti numbers, over an arbitrary field, of the ordered configuration spaces of a graph. In characteristic zero, we further give explicit formulas for the asymptotic multiplicities in homology of many irreducible representations of the symmetric group, in the spirit of representation stability.

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Louis Hainaut, Ben Knudsen, Nicholas Wawrykow. 2025-09-30. Representation asymptotics in the homology of pure graph braid groups. https://arxiv.org/abs/2510.00201

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