PreprintarXiv licencearXiv
Non-maximal quasi-isometric PU2,n+1-representations via alternating surfaces in complex pseudo-hyperbolic spaces
Abstract
For every admissible non-maximal Toledo invariant t, we construct a locus of irreducible representations of a closed genus-g surface group into PU2,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 ∂-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 S2n−1× S2n−1.
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BibTeX
@misc{li2026nonmaximal,
title = {{Non-maximal quasi-isometric $\mathrmPU_2,n+1$-representations via alternating surfaces in complex pseudo-hyperbolic spaces}},
author = {Qiongling Li and Junming Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.24672},
eprint = {2609.24672},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24672},
}
RIS
TY - UNPB
TI - Non-maximal quasi-isometric PU_2,n+1-representations via alternating surfaces in complex pseudo-hyperbolic spaces
AU - Qiongling Li
AU - Junming Zhang
PY - 2026
DA - 2026/10/24
PB - arXiv
DO - 10.48550/arxiv.2609.24672
UR - https://arxiv.org/abs/2609.24672
AB - For every admissible non-maximal Toledo invariant t, we construct a locus of irreducible representations of a closed genus-g surface group into 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 ∂-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× S^2n−1.
ER -