An unoriented skein relation via bordered–sutured Floer homology

Document Type

Article

Publication Date

1-1-2021

Abstract

We show that the bordered–sutured Floer invariant of the com-plement of a tangle in an arbitrary 3-manifold Y, with minimal conditions on the bordered–sutured structure, satisfies an unori-ented skein exact triangle. This generalizes a theorem by Manolescu [Man07] for links in S3. We give a theoretical proof of this result by adapting holomorphic polygon counts to the bordered–sutured set-ting, and also give a combinatorial description of all maps involved and explicitly compute them. We then show that, for Y = S3, our exact triangle coincides with Manolescu’s. Finally, we provide a graded version of our result, explaining in detail the grading reduction process involved.

Publication Source (Journal or Book title)

Journal of Symplectic Geometry

First Page

1495

Last Page

1561

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