{"paper":{"title":"Actions of solvable Baumslag-Solitar groups on surfaces with (pseudo-)Anosov elements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Juan Alonso, Juliana Xavier, Nancy Guelman","submitted_at":"2013-10-09T13:19:57Z","abstract_excerpt":"Let $BS(1,n)= <a,b : a b a ^{-1} = b ^n>$ be the solvable Baumslag-Solitar group, where $n \\geq 2$. We study representations of $BS(1, n)$ by homeomorphisms of closed surfaces with (pseudo-)Anosov elements. That is, we consider a closed surface $S$, and homeomorphisms $f, h: S \\to S$ such that $h f h^{-1} = f^n$, for some $ n\\geq 2$. It is known that $f$ (or some power of $f$) must be homotopic to the identity. Suppose that $h$ is pseudo-Anosov with stretch factor $\\lambda >1$. We show that $<f,h>$ is not a faithful representation of $BS(1, n)$ if $\\lambda > n$. Moreover, we show that there ar"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.2465","kind":"arxiv","version":3},"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"}