We use cookies to ensure that we give you the best experience on our website. You can change your cookie settings at any time. Otherwise, we'll assume you're OK to continue.

Durham University

Department of Mathematical Sciences

Academic Staff

Publication details for Pavel Tumarkin

Felikson, A. & Tumarkin, P. (2019). Geometry of mutation classes of rank 3 quivers. Arnold Mathematical Journal

Author(s) from Durham


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 π-rotations for the cyclic ones. The geometric behavior
of the model turns out to be controlled by the Markov constant p2 + q2 + r 2 − pqr,
where p, q,r are the weights of arrows in a quiver. We also classify skew-symmetric
mutation-finite real 3×3 matrices and explore the structure of acyclic representatives
in finite and infinite mutation classes.