发表机构
Chern Institute of Mathematics and LPMC, Nankai University（南开大学陈省身数学研究所和LPMC）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文为每个可容许非极大Toledo不变量构造了曲面群到$\mathrm{PU}_{2,n+1}$的不可约表示，其轨道映射为拟等距嵌入，并构造了Shilov边界上的不连续域，商为纤维丛。
AI 中文摘要
对于每个可容许的非极大Toledo不变量 $t$，我们构造了一个闭亏格 $g$ 曲面群到 $\mathrm{PU}_{2,n+1}$ 的不可约表示轨迹，其Toledo不变量为 $t$，且轨道映射是拟等距嵌入。这些轨迹在特征簇中的实余维数根据Toledo值分别为 $10(g-1)$ 或 $10(g-1)+2(n-1)$。我们的构造使用了 $4$-循环Higgs丛及其与复伪双曲空间中 $\partial$-交替曲面的对应关系。相关的等变极小映射到对称空间是双Lipschitz嵌入。我们进一步在Shilov边界构造了余紧致的不连续域。它们的商是曲面上的光滑纤维丛，纤维同胚于 $S^{2n-1}\times S^{2n-1}$。
英文摘要
For every admissible non-maximal Toledo invariant $t$, we construct a locus of irreducible representations of a closed genus-$g$ surface group into $\mathrm{PU}_{2,n+1}$ with Toledo invariant $t$ whose orbit maps are quasi-isometric embeddings. These loci have real codimension $10(g-1)$ or $10(g-1)+2(n-1)$ in the character variety depending on the Toledo value. Our construction uses $4$-cyclic Higgs bundles and their correspondence with $\partial$-alternating surfaces in complex pseudo-hyperbolic spaces. The associated equivariant minimal maps into the symmetric space are bi-Lipschitz embeddings. We further construct cocompact domains of discontinuity in the Shilov boundary. Their quotients are smooth fiber bundles over the surface with fiber homeomorphic to $S^{2n-1}\times S^{2n-1}$.
Comments55 pages, including two appendices and a declaration of AI use, comments are very welcome
