{"title":"来自抓握器的打结家庭","authors":"Danica Kosanović","doi":"10.1112/topo.12337","DOIUrl":null,"url":null,"abstract":"<p>For any smooth manifold <span></span><math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math> of dimension <span></span><math>\n <semantics>\n <mrow>\n <mi>d</mi>\n <mo>⩾</mo>\n <mn>4</mn>\n </mrow>\n <annotation>$d\\geqslant 4$</annotation>\n </semantics></math>, we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into <span></span><math>\n <semantics>\n <mi>M</mi>\n <annotation>$M$</annotation>\n </semantics></math>, in every degree that is a multiple of <span></span><math>\n <semantics>\n <mrow>\n <mi>d</mi>\n <mo>−</mo>\n <mn>3</mn>\n </mrow>\n <annotation>$d-3$</annotation>\n </semantics></math>, and show that they are detected in the Taylor tower of Goodwillie and Weiss. The classes are obtained from families of string links constructed in the <span></span><math>\n <semantics>\n <mi>d</mi>\n <annotation>$d$</annotation>\n </semantics></math>-ball.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2024-05-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12337","citationCount":"0","resultStr":"{\"title\":\"Knotted families from graspers\",\"authors\":\"Danica Kosanović\",\"doi\":\"10.1112/topo.12337\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>For any smooth manifold <span></span><math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math> of dimension <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>d</mi>\\n <mo>⩾</mo>\\n <mn>4</mn>\\n </mrow>\\n <annotation>$d\\\\geqslant 4$</annotation>\\n </semantics></math>, we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into <span></span><math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$M$</annotation>\\n </semantics></math>, in every degree that is a multiple of <span></span><math>\\n <semantics>\\n <mrow>\\n <mi>d</mi>\\n <mo>−</mo>\\n <mn>3</mn>\\n </mrow>\\n <annotation>$d-3$</annotation>\\n </semantics></math>, and show that they are detected in the Taylor tower of Goodwillie and Weiss. The classes are obtained from families of string links constructed in the <span></span><math>\\n <semantics>\\n <mi>d</mi>\\n <annotation>$d$</annotation>\\n </semantics></math>-ball.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2024-05-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12337\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12337\",\"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.12337","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
对于维度为 d ⩾ 4 $d\geqslant 4$ 的任何光滑流形 M $M$，我们在弧或圆嵌入 M $M$的空间的同调群中，在每一个度数为 d - 3 $d-3$ 的倍数中构造了明确的类，并证明它们在古德威利和韦斯的泰勒塔中被检测到。这些类是从在 d $d$ 球中构造的弦链接族中获得的。
For any smooth manifold of dimension , we construct explicit classes in homotopy groups of spaces of embeddings of either an arc or a circle into , in every degree that is a multiple of , and show that they are detected in the Taylor tower of Goodwillie and Weiss. The classes are obtained from families of string links constructed in the -ball.
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