Browsing by Subject "KNOTS"

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    A slicing obstruction from the $\frac {10}{8}$ theorem
    (Proceedings of the American Mathematical Society, 2016-08-29) Donald, A; Vafaee, F
    © 2016 American Mathematical Society. From Furuta’s 10/8 theorem, we derive a smooth slicing obstruction for knots in S3 using a spin 4-manifold whose boundary is 0-surgery on a knot. We show that this obstruction is able to detect torsion elements in the smooth concordance group and find topologically slice knots which are not smoothly slice.
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    Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic
    (Topology and its Applications, 2015-04) Vafaee, F
    © 2015 Elsevier B.V. In this paper we find a family of knots with trivial Alexander polynomial, and construct two non-isotopic Seifert surfaces for each member in our family. In order to distinguish the surfaces we study the sutured Floer homology invariants of the sutured manifolds obtained by cutting the knot complements along the Seifert surfaces. Our examples provide the first use of sutured Floer homology, and not merely its Euler characteristic (a classical torsion), to distinguish Seifert surfaces. Our technique uses a version of Floer homology, called ". longitude Floer homology" in a way that enables us to bypass the computations related to the SFH of the complement of a Seifert surface.
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    The cardinality of the augmentation category of a Legendrian link
    (Mathematical Research Letters, 2017) Ng, L; Rutherford, D; Shende, V; Sivek, S
    We introduce a notion of cardinality for the augmentation category associated to a Legendrian knot or link in standard contact R3. This ℓhomotopy cardinality' is an invariant of the category and allows for a weighted count of augmentations, which we prove to be determined by the ruling polynomial of the link. We present an application to the augmentation category of doubly Lagrangian slice knots.