Browsing by Subject "HOLOMORPHIC DISKS"

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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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    Berge–Gabai knots and L–space satellite operations
    (Algebraic & Geometric Topology, 2015-01-15) Hom, J; Lidman, T; Vafaee, F
    © 2014 Mathematical Sciences Publishers. All rights reserved. Let P(K) be a satellite knot where the pattern P is a Berge–Gabai knot (ie a knot in the solid torus with a nontrivial solid torus Dehn surgery) and the companion K is a nontrivial knot in S3. We prove that P(K) is an L–space knot if and only if K is an L–space knot and P is sufficiently positively twisted relative to the genus of K. This generalizes the result for cables due to Hedden [13] and Hom [17].
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    On the Knot Floer Homology of Twisted Torus Knots
    (International Mathematics Research Notices, 2015) Vafaee, F
    © 2014 The Author(s) 2014. Published by Oxford University Press. All rights reserved. For permissions, please e-mail: journals.permissions@oup.com. In this paper, we study the knot Floer homology of a subfamily of twisted (p,q) torus knots where q=plusmn;1 (mod p). Specifically, we classify the knots in this subfamily that admit L-space surgeries. To do calculations, we use the fact that these knots are (1,1) knots and, therefore, admit a genus one Heegaard diagram.