{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ETOGRF3DOKPY6OPLFCODWBWXFG","short_pith_number":"pith:ETOGRF3D","schema_version":"1.0","canonical_sha256":"24dc689763729f8f39eb289c3b06d72995cd9d9db24704e2c768f6d740593fc9","source":{"kind":"arxiv","id":"1310.2465","version":3},"attestation_state":"computed","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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.2465","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2013-10-09T13:19:57Z","cross_cats_sorted":[],"title_canon_sha256":"8b523002ab4ff6c3269e5fc909eccdbbb7e0c62341842964f6e1d7cabdd863f0","abstract_canon_sha256":"3329933597c617b10c1a4892cb70a9e2faba15aac90c7961a6780b3848d9db3e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:51:08.371535Z","signature_b64":"xy14qlKIiezMgCr88ZLzf0+MQfFuJsfLq4OmnG5lJSCT+yTuF0JDJuIK74GS8WPeUnsjd/djzDae0ka468ZmCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"24dc689763729f8f39eb289c3b06d72995cd9d9db24704e2c768f6d740593fc9","last_reissued_at":"2026-05-18T02:51:08.371043Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:51:08.371043Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $\\lambda > n$. 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