{"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":56114,"journal":{"name":"Journal of Topology","volume":"17 2","pages":""},"PeriodicalIF":0.8000,"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\":56114,\"journal\":{\"name\":\"Journal of Topology\",\"volume\":\"17 2\",\"pages\":\"\"},\"PeriodicalIF\":0.8000,\"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\":\"Journal of Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12337\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12337","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","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.
期刊介绍：
The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal.
The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.
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