Homotopy groups of moduli spaces of stable quiver representations

Graeme Wilkin

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arXiv · 0901.4156

Homotopy groups of moduli spaces of stable quiver representations

Graeme Wilkin

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Abstract

The purpose of this paper is to describe a method for computing homotopy groups of the space of $α$-stable representations of a quiver with fixed dimension vector and stability parameter $α$. 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 $α$-stable representations of the quiver with fixed dimension vector, and apply the theory to the space of non-degenerate polygons in three-dimensional Euclidean space.

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BibTeX RIS

Graeme Wilkin. 2009-10-27. Homotopy groups of moduli spaces of stable quiver representations. https://arxiv.org/abs/0901.4156

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