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Localization in quiver moduli spaces

Torus fixed points of quiver moduli spaces are given by stable representations of the universal (abelian) covering quiver. As far as the Kronecker quiver is concerned they can be described by stable representations of certain bipartite quivers coming along with a stable colouring. By use of the glueing method it is possible to construct a huge class of such quivers implying a lower bound for the Euler characteristic. For certain roots it is even possible to construct all torus fixed points.