Auslander Reiten quivers of type A(n) and B(n) can be viewed as braid diagrams and cluster mutations can be seen as homotopies of these braids. These are examples of more general theorems about the "dual braid monoid" and exceptional sequences proved by Bessis, Brady-Watt, Ingalls-Thomas and myself with Ralf Schiffler.
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Moscow MV Lomonosov State Univ, Chair Differential Geometry & Applicat, Moscow, RussiaMoscow MV Lomonosov State Univ, Chair Differential Geometry & Applicat, Moscow, Russia
Fedoseev, Denis A.
Manturov, Vassily O.
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Bauman Moscow State Tech Univ, Chair FN 12, Moscow, RussiaMoscow MV Lomonosov State Univ, Chair Differential Geometry & Applicat, Moscow, Russia
Manturov, Vassily O.
Cheng, Zhiyun
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Beijing Normal Univ, Lab Math & Complex Syst, Sch Math Sci, Minist Educ, Beijing 100875, Peoples R ChinaMoscow MV Lomonosov State Univ, Chair Differential Geometry & Applicat, Moscow, Russia