An application of the theory of FI -algebras to graph configuration spaces

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Abstract

Recent work of An et al. (Subdivisional spaces and graph braid groups. arXiv:1708.02351, 2019), as well as Ramos (Algebraic Geom Topol. arXiv:1609.05611, 2018), has shown that the homology groups of configuration spaces of graphs can be equipped with the structure of a finitely generated graded module over a polynomial ring. In this work we study this module structure in certain families of graphs using the language of FI-algebras recently explored by Nagel and Römer (FI- and OI-modules with varying coefficients. arXiv:1710.09247, 2017). As an application we prove that the syzygies of the modules in these families exhibit a range of stable behaviors.

Original languageEnglish
Pages (from-to)1-15
Number of pages15
JournalMathematische Zeitschrift
Volume294
Issue number1-2
DOIs
StatePublished - 1 Feb 2020

Keywords

  • FI-modules
  • Graph configuration spaces

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