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arXiv · 2407.07854

Abrams' stabilization theorem for no-k-equal configuration spaces on graphs

Omar Alvarado-Garduño·Jesús González
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Abstract

For a graph $G$, let Conf$(G,n)$ denote the classical configuration space of $n$ labelled points in $G$. Abrams introduced a cubical complex, denoted here by DConf$(G,n)$, sitting inside Conf$(G,n)$ as a strong deformation retract provided $G$ is suitably subdivided. Using discrete Morse Theory techniques, we extend Abrams' result to the realm of configurations having no $k$-fold collisions.

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Omar Alvarado-Garduño, Jesús González. 2024-07-10. Abrams' stabilization theorem for no-k-equal configuration spaces on graphs. https://doi.org/10.4310/hha.2026.v28.n1.a1

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