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...boundary component has exactly one marked point, and used it to classify the surfaces (S,M) such that any two triangulations T1, T2 of (S,M) give rise to derived equivalent algebras BT1 and BT2 , see =-=[24]-=-. Let us also mention that the AG-invariant has been used by Bobinski and Buan in [11] to classify algebras that are derived equivalent to cluster-tilted algebras of type A and Ã. We then study the m...

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...itly. An explicit construction for adjacency quivers of triangulations has been given by Labardini [20]. For the exceptional mutation classes that are not acyclic, potentials can be found in our work =-=[21]-=-. The rest of this section is devoted to the proof of Theorem 4.11. We start by recording the following observation. Lemma 4.15. If Q has a sink i and Q \ {i} belongs to P, then Q belongs to P. ON CLU...

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...urface (up to isotopy) such that f induces a quiver automorphism on QT and (χ1, f (χ2)) or ( f (χ1),χ2) are equi-distributed. Related work has been done for unpunctured surfaces without cuts. Ladkani =-=[17]-=- uses quiver mutation to characterize the surfaces such that all the algebras arising from their triangulations are derived equivalent. Bobinski and Buan [8] classified the gentle algebras that are de...

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...the 1 2 (1, 2)⊕ 1 2 (3, 2) representation of the SU(2)diag × SU(2)3rd boundary gauge subgroup. A convenient recipe to produce explicit quivers in each of the classes Cg,b can be found in section 3 of =-=[41]-=-. For quivers arising from triangulations of surfaces Cg,b the total number of arrows #Q1 = 12(g − 1) + 7b is an invariant under mutations, a feature of all SU(2)k half–hypers models, but X6 [42]. Sin...