# Browsing by Subject "HOLOMORPHIC DISKS"

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Item Open Access 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.Item Open Access 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].Item Open Access 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.