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

2023/05/30 by Knudsen, Ben, Ramos, Eric · 2 citations
#Algebraic Topology (math.AT) #Category Theory (math.CT) #Combinatorics (math.CO) #FOS: Mathematics #Geometric Topology (math.GT)

paper · doi:10.48550/arxiv.2305.19363

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.

Cited by

• Representation asymptotics in the homology of pure graph braid groups
• Hilbert Series for Configuration Spaces of Punctured Surfaces

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