Abrams' stabilization theorem for no-k-equal configuration spaces on graphs
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866914271227543552 |
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| author | Alvarado-Garduño, Omar González, Jesús |
| author_facet | Alvarado-Garduño, Omar González, Jesús |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07854 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Abrams' stabilization theorem for no-k-equal configuration spaces on graphs Alvarado-Garduño, Omar González, Jesús Algebraic Topology Combinatorics 20F36, 20F65, 55P10, 55R80 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. |
| title | Abrams' stabilization theorem for no-k-equal configuration spaces on graphs |
| topic | Algebraic Topology Combinatorics 20F36, 20F65, 55P10, 55R80 |
| url | https://arxiv.org/abs/2407.07854 |