Robertson's conjecture and universal finite generation in the homology of graph braid groups

Ben Knudsen; Eric Ramos

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arXiv · 2305.19363

Robertson's conjecture and universal finite generation in the homology of graph braid groups

Ben Knudsen·Eric Ramos

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Abstract

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.

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Ben Knudsen, Eric Ramos. 2023-05-30. Robertson's conjecture and universal finite generation in the homology of graph braid groups. https://arxiv.org/abs/2305.19363

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