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An unoriented skein relation via bordered-sutured Floer homology

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 Added by C.-M. Michael Wong
 Publication date 2018
  fields
and research's language is English




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We show that the bordered-sutured Floer invariant of the complement of a tangle in an arbitrary 3-manifold $Y$, with minimal conditions on the bordered-sutured structure, satisfies an unoriented skein exact triangle. This generalizes a theorem by Manolescu for links in $S^3$. We give a theoretical proof of this result by adapting holomorphic polygon counts to the bordered-sutured setting, and also give a combinatorial description of all maps involved and explicitly compute them. We then show that, for $Y = S^3$, our exact triangle coincides with Manolescus. Finally, we provide a graded version of our result, explaining in detail the grading reduction process involved.



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137 - C.-M. Michael Wong 2013
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