{"title":"双点增强网格同构性质的组合证明","authors":"Ollie Thakar","doi":"10.4153/s0008414x23000809","DOIUrl":null,"url":null,"abstract":"<p>We provide a purely combinatorial proof of a skein exact sequence obeyed by double-point enhanced grid homology. We also extend the theory to coefficients over <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231220175033308-0060:S0008414X23000809:S0008414X23000809_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$\\mathbb {Z},$</span></span></img></span></span> and discuss alternatives to the Ozsváth–Szabó <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231220175033308-0060:S0008414X23000809:S0008414X23000809_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$\\tau $</span></span></img></span></span> invariant.</p>","PeriodicalId":501820,"journal":{"name":"Canadian Journal of Mathematics","volume":"31 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2023-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Combinatorial proofs of properties of double-point enhanced grid homology\",\"authors\":\"Ollie Thakar\",\"doi\":\"10.4153/s0008414x23000809\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We provide a purely combinatorial proof of a skein exact sequence obeyed by double-point enhanced grid homology. We also extend the theory to coefficients over <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231220175033308-0060:S0008414X23000809:S0008414X23000809_inline1.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\mathbb {Z},$</span></span></img></span></span> and discuss alternatives to the Ozsváth–Szabó <span><span><img data-mimesubtype=\\\"png\\\" data-type=\\\"\\\" src=\\\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231220175033308-0060:S0008414X23000809:S0008414X23000809_inline2.png\\\"><span data-mathjax-type=\\\"texmath\\\"><span>$\\\\tau $</span></span></img></span></span> invariant.</p>\",\"PeriodicalId\":501820,\"journal\":{\"name\":\"Canadian Journal of Mathematics\",\"volume\":\"31 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2023-12-05\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Canadian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4153/s0008414x23000809\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Canadian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4153/s0008414x23000809","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Combinatorial proofs of properties of double-point enhanced grid homology
We provide a purely combinatorial proof of a skein exact sequence obeyed by double-point enhanced grid homology. We also extend the theory to coefficients over $\mathbb {Z},$ and discuss alternatives to the Ozsváth–Szabó $\tau $ invariant.
$\mathbb {Z},$ and discuss alternatives to the Ozsváth–Szabó 
$\tau $ invariant.
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