稳定双表示的模空间的同伦群
Homotopy groups of moduli spaces of stable quiver representations
摘要：
本文的目的是描述一种计算具有固定维数向量和稳定性参数$α$的图的$α$ -稳定表示空间的同伦群的方法。主要结果是：该空间的同伦群在一定维数下是平凡的，这取决于维数、维数向量的选择和参数的选择。作为推论，我们还计算了具有固定维数向量的多项式的$α$ -稳定表示的模空间的低维同伦群，并将理论应用于三维欧几里得空间中的非退化多边形空间。
英文摘要：
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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