Quivers with potentials associated with triangulations of Riemann surfaces
Permanent URL:
http://hdl.handle.net/2047/d20000727
Weyman, Jerzy M. (Committee member)
Todorov, Gordana G. (Committee member)
Derksen, Harm (Committee member)
In Part I we associate to each ideal triangulation of a bordered surface with marked points a quiver with potential, in such a way that whenever two ideal triangulations are related by a flip of an arc, the respective quivers with potentials are related by a mutation with respect to the flipped arc. We prove that if the surface has non-empty boundary, then the quivers with potentials associated to its triangulations are rigid and hence non-degenerate, and have finite-dimensional Jacobian algebra.
In Part II we define, given an arc and an ideal triangulation of a bordered marked surface, a representation of the quiver with potential constructed in Part I, so that whenever two ideal triangulations are related by a flip, the associated representations are related by the corresponding mutation of representations.
flip
mutation
potential
quiver
representation
triangulation
Mathematics
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