双曲结补商的尖型

Proceedings of the American Mathematical Society, Series B Pub Date : 2020-01-14 DOI:10.1090/bproc/104

Neil R. Hoffman

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Furthermore, if a knot complement covers an orbifold with a <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S squared left-parenthesis 2 comma 3 comma 6 right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:msup>\n <mml:mi>S</mml:mi>\n <mml:mn>2</mml:mn>\n </mml:msup>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mn>2</mml:mn>\n <mml:mo>,</mml:mo>\n <mml:mn>3</mml:mn>\n <mml:mo>,</mml:mo>\n <mml:mn>6</mml:mn>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">S^2(2,3,6)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> cusp, it also covers an orbifold with a <inline-formula content-type=\"math/mathml\">\n<mml:math xmlns:mml=\"http://www.w3.org/1998/Math/MathML\" alttext=\"upper S squared left-parenthesis 3 comma 3 comma 3 right-parenthesis\">\n <mml:semantics>\n <mml:mrow>\n <mml:msup>\n <mml:mi>S</mml:mi>\n <mml:mn>2</mml:mn>\n </mml:msup>\n <mml:mo stretchy=\"false\">(</mml:mo>\n <mml:mn>3</mml:mn>\n <mml:mo>,</mml:mo>\n <mml:mn>3</mml:mn>\n <mml:mo>,</mml:mo>\n <mml:mn>3</mml:mn>\n <mml:mo stretchy=\"false\">)</mml:mo>\n </mml:mrow>\n <mml:annotation encoding=\"application/x-tex\">S^2(3,3,3)</mml:annotation>\n </mml:semantics>\n</mml:math>\n</inline-formula> cusp. We end with a discussion that shows all cusp types arise in the quotients of link complements.</p>","PeriodicalId":106316,"journal":{"name":"Proceedings of the American Mathematical Society, Series B","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Cusp types of quotients of hyperbolic knot complements\",\"authors\":\"Neil R. Hoffman\",\"doi\":\"10.1090/bproc/104\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>This paper completes a classification of the types of orientable and non-orientable cusps that can arise in the quotients of hyperbolic knot complements. In particular, <inline-formula content-type=\\\"math/mathml\\\">\\n<mml:math xmlns:mml=\\\"http://www.w3.org/1998/Math/MathML\\\" alttext=\\\"upper S squared left-parenthesis 2 comma 4 comma 4 right-parenthesis\\\">\\n <mml:semantics>\\n <mml:mrow>\\n <mml:msup>\\n <mml:mi>S</mml:mi>\\n <mml:mn>2</mml:mn>\\n </mml:msup>\\n <mml:mo stretchy=\\\"false\\\">(</mml:mo>\\n <mml:mn>2</mml:mn>\\n <mml:mo>,</mml:mo>\\n <mml:mn>4</mml:mn>\\n <mml:mo>,</mml:mo>\\n <mml:mn>4</mml:mn>\\n <mml:mo stretchy=\\\"false\\\">)</mml:mo>\\n </mml:mrow>\\n <mml:annotation encoding=\\\"application/x-tex\\\">S^2(2,4,4)</mml:annotation>\\n </mml:semantics>\\n</mml:math>\\n</inline-formula> cannot be the cusp cross-section of any orbifold quotient of a hyperbolic knot complement. 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引用次数: 2

摘要

本文完成了双曲结补商中可定向尖和不可定向尖的分类。特别地，s2 (2,4,4) S^2(2,4,4)不可能是双曲结补的任何轨道商的尖截面。更进一步，如果一个结补覆盖了一个具有s2 (2,3,6) S²(2,3,6)尖的轨道，它也覆盖了一个具有s2 (3,3,3) S²(3,3,3)尖的轨道。我们最后的讨论表明，所有尖音类型出现在连接补语的商。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Cusp types of quotients of hyperbolic knot complements

This paper completes a classification of the types of orientable and non-orientable cusps that can arise in the quotients of hyperbolic knot complements. In particular, S 2 ( 2 , 4 , 4 ) S^2(2,4,4) cannot be the cusp cross-section of any orbifold quotient of a hyperbolic knot complement. Furthermore, if a knot complement covers an orbifold with a S 2 ( 2 , 3 , 6 ) S^2(2,3,6) cusp, it also covers an orbifold with a S 2 ( 3 , 3 , 3 ) S^2(3,3,3) cusp. We end with a discussion that shows all cusp types arise in the quotients of link complements.

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来源期刊

Proceedings of the American Mathematical Society, Series B

CiteScore

1.60

自引率

0.00%

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