{"paper":{"title":"Well-rounded equivariant deformation retracts of Teichm\\\"uller spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Lizhen Ji","submitted_at":"2013-02-04T21:43:41Z","abstract_excerpt":"In this paper, we construct spines, i.e., $\\Mod_g$-equivariant deformation retracts, of the Teichm\\\"uller space $\\T_g$ of compact Riemann surfaces of genus $g$. Specifically, we define a $\\Mod_g$-stable subspace $S$ of positive codimension and construct an intrinsic $\\Mod_g$-equivariant deformation retraction from $\\T_g$ to $S$. As an essential part of the proof, we construct a canonical $\\Mod_g$-deformation retraction of the Teichm\\\"uller space $\\T_g$ to its thick part $\\T_g(\\varepsilon)$ when $\\varepsilon$ is sufficiently small. These equivariant deformation retracts of $\\T_g$ give cocompact"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.0877","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"}