Geometry of Mutation Classes of Rank 3 Quivers

  title={Geometry of Mutation Classes of Rank 3 Quivers},
  author={A. A. Felikson and Pavel Tumarkin},
  journal={Arnold Mathematical Journal},
We present a geometric realization for all mutation classes of quivers of rank 3 with real weights. This realization is via linear reflection groups for acyclic mutation classes and via groups generated by $$\pi $$π-rotations for the cyclic ones. The geometric behavior of the model turns out to be controlled by the Markov constant $$p^2+q^2+r^2-pqr$$p2+q2+r2-pqr, where p, q, r are the weights of arrows in a quiver. We also classify skew-symmetric mutation-finite real $$3\times 3$$3×3 matrices… 
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