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

• Ben Knudsen ^[1] ; Eric Ramos ^[2]
  1. [1] Northeastern University

     Northeastern University

     City of Boston, Estados Unidos

     
  2. [2] Stevens Institute of Technology

     Stevens Institute of Technology

     City of Hoboken, Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 5, 2024
• Idioma: inglés
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• Resumen

  • We formulate a categorification of Robertson’s conjecture analogous to the categorical graph minor conjecture of Miyata–Proudfoot–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 Proudfoot–Ramos, implying that the category of cographs is Noetherian, a result of potential independent interest.