Robertson's conjecture and universal finite generation in the homology of graph braid groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866911883568611328 |
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| author | Knudsen, Ben Ramos, Eric |
| author_facet | Knudsen, Ben Ramos, Eric |
| contents | We formulate a categorification of Robertson's conjecture analogous to the categorical graph minor conjecture of Miyata--Proudfood--Ramos. We show that these conjectures imply the existence of a finite list of atomic graphs generating the homology of configuration spaces of graphs -- in fixed degree, with a fixed number of particles, under topological embeddings. We explain how the simplest case of our conjecture follows from work of Barter and Miyata--Proudfoot, implying that the category of cographs is Noetherian, a result of potential independent interest. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_19363 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Robertson's conjecture and universal finite generation in the homology of graph braid groups Knudsen, Ben Ramos, Eric Algebraic Topology Combinatorics Category Theory Geometric Topology We formulate a categorification of Robertson's conjecture analogous to the categorical graph minor conjecture of Miyata--Proudfood--Ramos. We show that these conjectures imply the existence of a finite list of atomic graphs generating the homology of configuration spaces of graphs -- in fixed degree, with a fixed number of particles, under topological embeddings. We explain how the simplest case of our conjecture follows from work of Barter and Miyata--Proudfoot, implying that the category of cographs is Noetherian, a result of potential independent interest. |
| title | Robertson's conjecture and universal finite generation in the homology of graph braid groups |
| topic | Algebraic Topology Combinatorics Category Theory Geometric Topology |
| url | https://arxiv.org/abs/2305.19363 |