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arXiv · 2607.11863

Magnitude homology of tope graphs

Junnosuke Koizumi
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Abstract

We completely determine the magnitude homology of tope graphs of real hyperplane arrangements. Their ranks can be described as the Hilbert functions of the Stanley--Reisner rings of certain simplicial complexes naturally associated with the arrangements. For Coxeter arrangements, this gives a computation of the magnitude homology of the Cayley graph of the corresponding Coxeter group. We also prove the homological reciprocity for central arrangements conjectured by Koizumi--Liu. The proof combines poset combinatorics, the Edelman--Walker theorem, and Alexander duality.

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Junnosuke Koizumi. 2026-07-13. Magnitude homology of tope graphs. https://arxiv.org/abs/2607.11863

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