TY - JOUR
T1 - An application of the theory of FI -algebras to graph configuration spaces
AU - Ramos, Eric
N1 - Publisher Copyright:
© 2019, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2020/2/1
Y1 - 2020/2/1
N2 - 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.
AB - 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.
KW - FI-modules
KW - Graph configuration spaces
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U2 - 10.1007/s00209-019-02278-w
DO - 10.1007/s00209-019-02278-w
M3 - Article
AN - SCOPUS:85064148210
SN - 0025-5874
VL - 294
SP - 1
EP - 15
JO - Mathematische Zeitschrift
JF - Mathematische Zeitschrift
IS - 1-2
ER -