{"title":"有纤维结的精梳属和复杂性","authors":"Mustafa Cengiz","doi":"10.1112/topo.12268","DOIUrl":null,"url":null,"abstract":"<p>We prove that if a fibered knot <math>\n <semantics>\n <mi>K</mi>\n <annotation>$K$</annotation>\n </semantics></math> with genus greater than 1 in a three-manifold <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> has a sufficiently complicated monodromy, then <math>\n <semantics>\n <mi>K</mi>\n <annotation>$K$</annotation>\n </semantics></math> induces a minimal genus Heegaard splitting <math>\n <semantics>\n <mi>P</mi>\n <annotation>$P$</annotation>\n </semantics></math> that is unique up to isotopy, and small genus Heegaard splittings of <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> are stabilizations of <math>\n <semantics>\n <mi>P</mi>\n <annotation>$P$</annotation>\n </semantics></math>. We provide a complexity bound in terms of the Heegaard genus of <math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math>. We also provide global complexity bounds for fibered knots in the three-sphere and lens spaces.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-11-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Heegaard genus and complexity of fibered knots\",\"authors\":\"Mustafa Cengiz\",\"doi\":\"10.1112/topo.12268\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We prove that if a fibered knot <math>\\n <semantics>\\n <mi>K</mi>\\n <annotation>$K$</annotation>\\n </semantics></math> with genus greater than 1 in a three-manifold <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math> has a sufficiently complicated monodromy, then <math>\\n <semantics>\\n <mi>K</mi>\\n <annotation>$K$</annotation>\\n </semantics></math> induces a minimal genus Heegaard splitting <math>\\n <semantics>\\n <mi>P</mi>\\n <annotation>$P$</annotation>\\n </semantics></math> that is unique up to isotopy, and small genus Heegaard splittings of <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math> are stabilizations of <math>\\n <semantics>\\n <mi>P</mi>\\n <annotation>$P$</annotation>\\n </semantics></math>. We provide a complexity bound in terms of the Heegaard genus of <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math>. We also provide global complexity bounds for fibered knots in the three-sphere and lens spaces.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2022-11-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12268\",\"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.12268","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that if a fibered knot with genus greater than 1 in a three-manifold has a sufficiently complicated monodromy, then induces a minimal genus Heegaard splitting that is unique up to isotopy, and small genus Heegaard splittings of are stabilizations of . We provide a complexity bound in terms of the Heegaard genus of . We also provide global complexity bounds for fibered knots in the three-sphere and lens spaces.
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