{"paper":{"title":"$d$-pleated surfaces and their shear-bend coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Filippo Mazzoli, Giuseppe Martone, Sara Maloni, Tengren Zhang","submitted_at":"2023-05-19T16:18:04Z","abstract_excerpt":"In this article, we single out representations of surface groups into $\\mathsf{PSL}_d(\\mathbb{C})$ which generalize the well-studied family of pleated surfaces into $\\mathsf{PSL}_2(\\mathbb{C})$. Our representations arise as sufficiently generic $\\lambda$-Borel Anosov representations, which are representations that are Borel Anosov with respect to a maximal geodesic lamination $\\lambda$. For fixed $\\lambda$ and $d$, we provide a holomorphic parametrization of the space $\\mathcal{R}(\\lambda,d)$ of $(\\lambda,d)$-pleated surfaces which extends both work of Bonahon for pleated surfaces and Bonahon "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2305.11780","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2305.11780/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}