自由群表示的模空间的拓扑
The topology of moduli spaces of free group representations
摘要：
对任意复仿射约化群G和固定的极大紧子群K的选择，证明了自由群的G-特征簇强形变收缩核到相应的K-特征空间，这是一个实半代数集.结合构造性不变量理论和经典拓扑方法，证明了秩2自由群的SL（3，C）-特征簇同伦于8球面，秩3自由群的SL（2，C）-特征簇同伦于6球面.
英文摘要：
For any complex affine reductive group G and a fixed choice of maximal compact subgroup K, we show that the G-character variety of a free group strongly deformation retracts to the corresponding K-character space, which is a real semi-algebraic set. Combining this with constructive invariant theory and classical topological methods, we show that the SL(3,C)-character variety of a rank 2 free group is homotopic to an 8 sphere and the SL(2,C)-character variety of a rank 3 free group is homotopic to a 6 sphere.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
