{"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}
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Abstract
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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