{"paper":{"title":"Roots of Dehn twists about separating curves","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Kashyap Rajeevsarathy","submitted_at":"2011-04-05T21:56:11Z","abstract_excerpt":"Let $C$ be a curve in a closed orientable surface $F$ of genus $g \\geq 2$ that separates $F$ into subsurfaces $\\widetilde {F_i}$ of genera $g_i$, for $i = 1,2$. We study the set of roots in $\\Mod(F)$ of the Dehn twist $t_C$ about $C$. All roots arise from pairs of $C_{n_i}$-actions on the $\\widetilde{F_i}$, where $n=\\lcm(n_1,n_2)$ is the degree of the root, that satisfy a certain compatibility condition. The $C_{n_i}$ actions are of a kind that we call nestled actions, and we classify them using tuples that we call data sets. The compatibility condition can be expressed by a simple formula, al"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.0968","kind":"arxiv","version":1},"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"}