{"title":"特征P$P$中sl(P)$\\mathfrak {sl}(P)$链路同源性的分离链路检测","authors":"Joshua Wang","doi":"10.1112/topo.12297","DOIUrl":null,"url":null,"abstract":"<p>We provide a sufficient condition for splitness of a link in terms of its reduced <math>\n <semantics>\n <mrow>\n <mi>sl</mi>\n <mo>(</mo>\n <mi>N</mi>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathfrak {sl}(N)$</annotation>\n </semantics></math> link homology with arbitrary field coefficients. The proof of sufficiency uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients. If <math>\n <semantics>\n <mi>N</mi>\n <annotation>$N$</annotation>\n </semantics></math> is prime and the coefficient field is of characteristic <math>\n <semantics>\n <mi>N</mi>\n <annotation>$N$</annotation>\n </semantics></math>, then the sufficient condition for splitness is also necessary. When <math>\n <semantics>\n <mrow>\n <mi>N</mi>\n <mo>=</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$N = 2$</annotation>\n </semantics></math>, we recover Lipshitz–Sarkar's split link detection result for Khovanov homology with <math>\n <semantics>\n <mrow>\n <mi>Z</mi>\n <mo>/</mo>\n <mn>2</mn>\n </mrow>\n <annotation>$\\mathbf {Z}/2$</annotation>\n </semantics></math> coefficients.</p>","PeriodicalId":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-05-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Split link detection for \\n \\n \\n sl\\n (\\n P\\n )\\n \\n $\\\\mathfrak {sl}(P)$\\n link homology in characteristic \\n \\n P\\n $P$\",\"authors\":\"Joshua Wang\",\"doi\":\"10.1112/topo.12297\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We provide a sufficient condition for splitness of a link in terms of its reduced <math>\\n <semantics>\\n <mrow>\\n <mi>sl</mi>\\n <mo>(</mo>\\n <mi>N</mi>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\mathfrak {sl}(N)$</annotation>\\n </semantics></math> link homology with arbitrary field coefficients. The proof of sufficiency uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients. If <math>\\n <semantics>\\n <mi>N</mi>\\n <annotation>$N$</annotation>\\n </semantics></math> is prime and the coefficient field is of characteristic <math>\\n <semantics>\\n <mi>N</mi>\\n <annotation>$N$</annotation>\\n </semantics></math>, then the sufficient condition for splitness is also necessary. When <math>\\n <semantics>\\n <mrow>\\n <mi>N</mi>\\n <mo>=</mo>\\n <mn>2</mn>\\n </mrow>\\n <annotation>$N = 2$</annotation>\\n </semantics></math>, we recover Lipshitz–Sarkar's split link detection result for Khovanov homology with <math>\\n <semantics>\\n <mrow>\\n <mi>Z</mi>\\n <mo>/</mo>\\n <mn>2</mn>\\n </mrow>\\n <annotation>$\\\\mathbf {Z}/2$</annotation>\\n </semantics></math> coefficients.</p>\",\"PeriodicalId\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"publicationDate\":\"2023-05-31\",\"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.12297\",\"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.12297","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Split link detection for
sl
(
P
)
$\mathfrak {sl}(P)$
link homology in characteristic
P
$P$
We provide a sufficient condition for splitness of a link in terms of its reduced link homology with arbitrary field coefficients. The proof of sufficiency uses Dowlin's spectral sequence and sutured Floer homology with twisted coefficients. If is prime and the coefficient field is of characteristic , then the sufficient condition for splitness is also necessary. When , we recover Lipshitz–Sarkar's split link detection result for Khovanov homology with coefficients.