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Skew-symmetric non-integer matrices with real entries can be viewed asquivers with non-integer weights of arrows. One can mutate such quiversaccording to usual rules of quiver mutation. Felikson and Tumarkin show thatrank 3 mutation-finite non-integer quivers admit geometric realisations bypartial reflections. This allows to define a notion of seeds (as Y-seeds), andhence, to define the exchange graphs for mutation classes. In this paper westudy exchange graphs of mutation-finite quivers in rank 3. The concept offinite and affine type generalises naturally to non-integer quivers. Inparticular, exchange graphs of finite type quivers are finite, while exchangegraphs of affine quivers are finite modulo the action of a finite-dimensionallattice.

Exchange graphs for mutation-finite non-integer quivers of rank 3