The Topology of the Space of Strictly Stable Representations of a Quiver

The purpose of this paper is to describe the topology of the space of strictly stable representations of a quiver with fixed dimension vector, where stability is defined with respect to a given parameter (which may be generic or non-generic). The main result is that the homotopy groups of this space are trivial up to a certain dimension, which depends on the quiver, the choice of dimension vector, and the choice of parameter. As a corollary we also compute low-dimensional homotopy groups of the moduli space of stable representations of the quiver with fixed dimension vector, and apply the theory to the space of non-degenerate polygons in R.