{"paper":{"title":"Isometric submersions of Teichm\\\"uller spaces are forgetful","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Dmitri Gekhtman, Mark Greenfield","submitted_at":"2019-01-09T03:07:24Z","abstract_excerpt":"We study the class of holomorphic and isometric submersions between finite-type Teichm\\\"uller spaces. We prove that, with potential exceptions coming from low-genus phenomena, any such map is a forgetful map $\\mathcal{T}_{g,n} \\rightarrow \\mathcal{T}_{g,m}$ obtained by filling in punctures. This generalizes a classical result of Royden and Earle-Kra asserting that biholomorphisms between finite-type Teichm\\\"uller spaces arise from mapping classes. As a key step in the argument, we prove that any $\\mathbb{C}$-linear embedding $Q(X)\\hookrightarrow Q(Y)$ between spaces of integrable quadratic dif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.02586","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":""},"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"}