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Recovering trees from the cohomology ring of their configuration spaces

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arxiv 2312.16646 v1 pith:ENXQTSVN submitted 2023-12-27 math.CO math.AT

Teresa I. Hoekstra-Mendoza This is my paper · ORCID
classification math.COmath.AT
keywords treebinarycohomologycomplexconfigurationringsimplicialalgebra
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abstract

Given a tree $T$, the cohomology ring of its unordered configuration space $H^{\ast}(U\mathcal{D}^nT)$ is an exterior face algebra if $T$ is a binary core tree (if by removing the leaves from $T$ we obtain a binary tree), or if $n=4$. This means that every cup product is determined by a simplicial complex $K_nT$. In this paper we show how to recover the tree $T$ from the simplicial complex $K_nT$ when $n=4.$

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Cited by 1 Pith paper

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  1. Edge-Span Chern Algebras of Graphical Configuration Spaces

    math.CO 2026-07 accept novelty 7.0 of 10

    The edge-span Chern algebra's cubic relation data is a complete tree invariant of polynomial size.

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