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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


The contraction category of graphs
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by Nicholas Proudfoot and Eric Ramos
Represent. Theory 26 (2022), 673-697
Published electronically: June 28, 2022


We study the category whose objects are graphs of fixed genus and whose morphisms are contractions. We show that the corresponding contravariant module categories are Noetherian and we study two families of modules over these categories. The first takes a graph to a graded piece of the homology of its unordered configuration space and the second takes a graph to an intersection homology group whose dimension is given by a Kazhdan–Lusztig coefficient; in both cases we prove that the module is finitely generated. This allows us to draw conclusions about torsion in the homology groups of graph configuration spaces, and about the growth of Betti numbers of graph configuration spaces and Kazhdan–Lusztig coefficients of graphical matroids. We also explore the relationship between our category and outer space, which is used in the study of outer automorphisms of free groups.
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Bibliographic Information
  • Nicholas Proudfoot
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403
  • MR Author ID: 689525
  • Email:
  • Eric Ramos
  • Affiliation: Department of Mathematics, Bowdoin College, Brunswick, Maine 04011
  • MR Author ID: 993563
  • Email:
  • Received by editor(s): July 18, 2020
  • Received by editor(s) in revised form: January 18, 2022, and April 21, 2022
  • Published electronically: June 28, 2022
  • Additional Notes: This work was supported by NSF grants DMS-1704811, DMS-1954050, DMS-2039316, DMS-2053243, and DMS-2137628.
  • © Copyright 2022 American Mathematical Society
  • Journal: Represent. Theory 26 (2022), 673-697
  • MSC (2020): Primary 05C25, 05C83, 14F43, 55R80
  • DOI:
  • MathSciNet review: 4445717