Representation asymptotics in the homology of pure graph braid groups
Algebraic Topology
2025-10-02 v1 Geometric Topology
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.
Keywords
Cite
@article{arxiv.2510.00201,
title = {Representation asymptotics in the homology of pure graph braid groups},
author = {Louis Hainaut and Ben Knudsen and Nicholas Wawrykow},
journal= {arXiv preprint arXiv:2510.00201},
year = {2025}
}
Comments
25 pages, 3 figures