Elizabeth Field, Heejoung Kim, Christopher Leininger, Marissa Loving
{"title":"映射tori的端周期同胚与体积","authors":"Elizabeth Field, Heejoung Kim, Christopher Leininger, Marissa Loving","doi":"10.1112/topo.12277","DOIUrl":null,"url":null,"abstract":"<p>Given an irreducible, end-periodic homeomorphism <math>\n <semantics>\n <mrow>\n <mi>f</mi>\n <mo>:</mo>\n <mi>S</mi>\n <mo>→</mo>\n <mi>S</mi>\n </mrow>\n <annotation>$f: S \\rightarrow S$</annotation>\n </semantics></math> of a surface with finitely many ends, all accumulated by genus, the mapping torus, <math>\n <semantics>\n <msub>\n <mi>M</mi>\n <mi>f</mi>\n </msub>\n <annotation>$M_f$</annotation>\n </semantics></math>, is the interior of a compact, irreducible, atoroidal 3-manifold <math>\n <semantics>\n <msub>\n <mover>\n <mi>M</mi>\n <mo>¯</mo>\n </mover>\n <mi>f</mi>\n </msub>\n <annotation>$\\overline{M}_f$</annotation>\n </semantics></math> with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of <math>\n <semantics>\n <msub>\n <mover>\n <mi>M</mi>\n <mo>¯</mo>\n </mover>\n <mi>f</mi>\n </msub>\n <annotation>$\\overline{M}_f$</annotation>\n </semantics></math> in terms of the translation length of <math>\n <semantics>\n <mi>f</mi>\n <annotation>$f$</annotation>\n </semantics></math> on the pants graph of <math>\n <semantics>\n <mi>S</mi>\n <annotation>$S$</annotation>\n </semantics></math>. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12277","citationCount":"7","resultStr":"{\"title\":\"End-periodic homeomorphisms and volumes of mapping tori\",\"authors\":\"Elizabeth Field, Heejoung Kim, Christopher Leininger, Marissa Loving\",\"doi\":\"10.1112/topo.12277\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Given an irreducible, end-periodic homeomorphism <math>\\n <semantics>\\n <mrow>\\n <mi>f</mi>\\n <mo>:</mo>\\n <mi>S</mi>\\n <mo>→</mo>\\n <mi>S</mi>\\n </mrow>\\n <annotation>$f: S \\\\rightarrow S$</annotation>\\n </semantics></math> of a surface with finitely many ends, all accumulated by genus, the mapping torus, <math>\\n <semantics>\\n <msub>\\n <mi>M</mi>\\n <mi>f</mi>\\n </msub>\\n <annotation>$M_f$</annotation>\\n </semantics></math>, is the interior of a compact, irreducible, atoroidal 3-manifold <math>\\n <semantics>\\n <msub>\\n <mover>\\n <mi>M</mi>\\n <mo>¯</mo>\\n </mover>\\n <mi>f</mi>\\n </msub>\\n <annotation>$\\\\overline{M}_f$</annotation>\\n </semantics></math> with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of <math>\\n <semantics>\\n <msub>\\n <mover>\\n <mi>M</mi>\\n <mo>¯</mo>\\n </mover>\\n <mi>f</mi>\\n </msub>\\n <annotation>$\\\\overline{M}_f$</annotation>\\n </semantics></math> in terms of the translation length of <math>\\n <semantics>\\n <mi>f</mi>\\n <annotation>$f$</annotation>\\n </semantics></math> on the pants graph of <math>\\n <semantics>\\n <mi>S</mi>\\n <annotation>$S$</annotation>\\n </semantics></math>. This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-01-06\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12277\",\"citationCount\":\"7\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12277\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12277","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
End-periodic homeomorphisms and volumes of mapping tori
Given an irreducible, end-periodic homeomorphism of a surface with finitely many ends, all accumulated by genus, the mapping torus, , is the interior of a compact, irreducible, atoroidal 3-manifold with incompressible boundary. Our main result is an upper bound on the infimal hyperbolic volume of in terms of the translation length of on the pants graph of . This builds on work of Brock and Agol in the finite-type setting. We also construct a broad class of examples of irreducible, end-periodic homeomorphisms and use them to show that our bound is asymptotically sharp.
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