{"title":"Localization and the Floer homology of strongly invertible knots","authors":"Aakash Parikh","doi":"arxiv-2408.13892","DOIUrl":null,"url":null,"abstract":"We establish two spectral sequences in knot Floer homology associated to a\ndirected strongly invertible knot K: one from the knot Floer homology of K to a\ntwo dimensional vector space, and one from the singular knot Floer homology of\na singular knot associated to K to the knot Floer homology quotient knot of K.\nThe first of these spectral sequences is used to define a numerical invariant\nof strongly invertible knots.","PeriodicalId":501271,"journal":{"name":"arXiv - MATH - Geometric Topology","volume":"13 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Geometric Topology","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2408.13892","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We establish two spectral sequences in knot Floer homology associated to a
directed strongly invertible knot K: one from the knot Floer homology of K to a
two dimensional vector space, and one from the singular knot Floer homology of
a singular knot associated to K to the knot Floer homology quotient knot of K.
The first of these spectral sequences is used to define a numerical invariant
of strongly invertible knots.
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