Braid groups and quiver mutation

Joseph Grant, Robert J. Marsh

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We describe presentations of braid groups of type ADE and show how these presentations are compatible with mutation of quivers, building on work of Barot and Marsh for Coxeter groups. In types A and D these presentations can be understood geometrically using triangulated surfaces. We then give a categorical interpretation of the presentations, with the new generators acting as spherical twists at simple modules on derived categories of Ginzburg dg-algebras of quivers with potential.
Original languageEnglish
Pages (from-to)77-116
Number of pages40
JournalPacific Journal of Mathematics
Issue number1
Publication statusPublished - 7 Jul 2017


  • mutation
  • braid groups
  • cluster algebras
  • Ginzburg dg algebra
  • spherical twist

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