Abrams' stabilization theorem for no-$k$-equal configuration spaces on graphs
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.
Fields of Study & Subjects
Advanced Topology and Set Theory
Publication details
- Journal / source
- Homology Homotopy and Applications
- Publisher
- International Press of Boston
- Volume
- 28
- Issue
- 1
- Pages
- 1–22
- Publication date
- 1 January 2026
- Language
- EN