{"title":"阳性辫子的特征谱","authors":"Sebastian Baader","doi":"10.24033/bsmf.2865","DOIUrl":null,"url":null,"abstract":"We derive a lower bound for all Levine-Tristram signatures of positive braid links, linear in terms of the first Betti number. As a consequence, we obtain upper and lower bounds on the ratio of fixed pairs of Levine-Tristram signature invariants, valid uniformly on all positive braid monoids.","PeriodicalId":55332,"journal":{"name":"Bulletin De La Societe Mathematique De France","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2023-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Signature spectrum of positive braids\",\"authors\":\"Sebastian Baader\",\"doi\":\"10.24033/bsmf.2865\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We derive a lower bound for all Levine-Tristram signatures of positive braid links, linear in terms of the first Betti number. As a consequence, we obtain upper and lower bounds on the ratio of fixed pairs of Levine-Tristram signature invariants, valid uniformly on all positive braid monoids.\",\"PeriodicalId\":55332,\"journal\":{\"name\":\"Bulletin De La Societe Mathematique De France\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2023-06-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Bulletin De La Societe Mathematique De France\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.24033/bsmf.2865\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Bulletin De La Societe Mathematique De France","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.24033/bsmf.2865","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
We derive a lower bound for all Levine-Tristram signatures of positive braid links, linear in terms of the first Betti number. As a consequence, we obtain upper and lower bounds on the ratio of fixed pairs of Levine-Tristram signature invariants, valid uniformly on all positive braid monoids.
期刊介绍：
The Bulletin de la Société Mathématique de France was founded in 1873, and it has published works by some of the most prestigious mathematicians, including for example H. Poincaré, E. Borel, E. Cartan, A. Grothendieck and J. Leray. It continues to be a journal of the highest mathematical quality, using a rigorous refereeing process, as well as a discerning selection procedure. Its editorial board members have diverse specializations in mathematics, ensuring that articles in all areas of mathematics are considered. Promising work by young authors is encouraged.
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