发表机构
Instituto de Matemáticas, Unidad Cuernavaca Universidad Nacional Autónoma de México（墨西哥国立自治大学库埃纳瓦瓦数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本研究构造了SU(2)×SU(2)上提升双曲环面自同构的实解析微分同胚，分析了其不变集、周期点性质、特征簇作用及本征流收敛性，排除了Anosov双曲性。
AI 中文摘要
我们通过在SU(2)²上计算自由群F₂的Nielsen自同构，构造了S³×S³≅SU(2)×SU(2)的实解析微分同胚，其提升了双曲环面自同构。GL(2,ℤ)中的每个矩阵都存在这样的提升，且所有提升都保持乘积Haar测度。对每个极大环面T⊂SU(2)，乘积T×T是不变的且承载原环面动力学；这些环面的并恰好是交换轨迹。同时共轭将环面周期点转化为周期共轭二维球面，排除了 ambient Anosov 双曲性。SU(2)特征簇上的诱导作用是典范的，在边界枕形上它是环面自同构在ξ↦-ξ下的商。最后，坐标三维闭链的归一化前向和后向像收敛到支撑在交换轨迹上的稳定和不稳定本征流。
英文摘要
We construct real-analytic diffeomorphisms of \(S^3\times S^3\cong \SU(2)\times\SU(2)\) that lift We study real-analytic word maps of \(S^3\times S^3\cong \SU(2)\times\SU(2)\) obtained by evaluating Nielsen automorphisms of the free group \(F_2\). Fried studied these word maps and computed their topological entropy. For each maximal torus \(T\subset\SU(2)\), the product \(T\times T\) is invariant and carries the corresponding toral dynamics. Their union is the commuting locus. We describe its regular part as a twisted conjugacy-sphere bundle over the punctured pillowcase and determine the local topology at the four central singularities. Periodic toral points give periodic conjugacy two-spheres, which obstruct Anosov hyperbolicity on \(S^3\times S^3\). Normalized images of the coordinate three-cycles converge to stable and unstable Ruelle--Sullivan eigencurrents supported on the commuting locus. The construction extends to \(\Sp(1)^n\). The higher-rank commuting locus has dimension \(n+2\), periodic conjugacy two-spheres persist, and the action on \(H_{3k}((S^3)^n)\) is \(Λ^k A\). For \(n\geq3\), IA-automorphisms can act nontrivially on the \(\SU(2)\)-character variety although they are trivial on abelianization. The degree-three eigencurrents again have a Ruelle--Sullivan description; higher exterior-power classes lead to a compactness problem for normal currents. We also relate the nonuniqueness of Nielsen lifts to Fried's computation of the mapping class group of \(S^3\times S^3\), where the group \(Θ_7\) of homotopy seven-spheres appears in the kernel of the action on homology.
CommentsNow the paper is 34 pages long. Important suggestions by Andrey Gogolev and Federico Rodríguez Hertz were included
