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This is a Quantitative Study study.

October 5, 2025Open Access

Representation asymptotics in the homology of pure graph braid groups

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Explicit formulas for asymptotic Betti numbers are derived for ordered configuration spaces of graphs, enhancing understanding of their homological properties.
In characteristic zero, the study also provides new insights into the asymptotic multiplicities of irreducible representations of the symmetric group.
The findings connect representation stability to the homological aspects of pure graph braid groups, revealing underlying patterns.
These results may have broader implications in the study of algebraic topology and representation theory.

Implication

This work demonstrates explicit formulas for Betti numbers and representation stability in symmetric groups, highlighting their significance in homology structures.

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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Cite This Study

Hainaut et al. (2025) studied this question.

synapsesocial.com/papers/68e24e6fd6d66a53c2473d96 https://doi.org/10.48550/arxiv.2510.00201

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Implication

This work demonstrates explicit formulas for Betti numbers and representation stability in symmetric groups, highlighting their significance in homology structures.

Representation asymptotics in the homology of pure graph braid groups

Key Points

Implication

Abstract

Discussion

Cite This Study

Representation asymptotics in the homology of pure graph braid groups

Key Points

Implication

Abstract

Discussion

Cite This Study

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