缺陷群与特征簇的拓扑
Flawed groups and the topology of character varieties
AI总结：
本文研究缺陷群，证明幂零群自由积的有限生成群为缺陷，推广已知类别，并给出RAAGs猜想证据及直积封闭性。
摘要：
一个有限表示的群F被称为缺陷的，如果对于约化仿射代数群G及其中的极大紧子群K，同态簇Hom(F,G)//G形变收缩到其子空间Hom(F,K)/K。在讨论了关于缺陷群的一般性之后，我们证明了所有同构于幂零群的自由积的有限生成群都是缺陷的。这统一并推广了所有先前已知的缺陷群类别。我们还为作者关于RAAGs（带挠）是缺陷的猜想提供了进一步证据。最后，我们证明了有限群与某些缺陷群的直积也是缺陷的。后两个定理扩大了已知的缺陷群类别。
英文摘要：
A finitely presented group F is called flawed if Hom(F,G)//G deformation retracts onto its subspace Hom(F,K)/K for reductive affine algebraic groups G and maximal compact subgroups K in G. After discussing generalities concerning flawed groups, we show that all finitely generated groups isomorphic to a free product of nilpotent groups are flawed. This unifies and generalizes all previously known classes of flawed groups. We also provide further evidence for the authors' conjecture that RAAGs (with torsion) are flawed. Lastly, we show direct products between finite groups and some flawed group are also flawed. These latter two theorems enlarge the known class of flawed groups.
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。
