Now showing items 1-8 of 8

    • (1,1) L-space knots 

      Greene, JE; Lewallen, S; Vafaee, F (COMPOSITIO MATHEMATICA, 2018-05-01)
      We characterize the (1, 1) knots in the three-sphere and lens spaces that admit non-trivial L-space surgeries. As a corollary, 1-bridge braids in these manifolds admit non- trivial L-space surgeries. We also recover ...
    • A slicing obstruction from the $\frac {10}{8}$ theorem 

      Donald, A; Vafaee, F (Proceedings of the American Mathematical Society, 2016-08-29)
      © 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 ...
    • Berge–Gabai knots and L–space satellite operations 

      Hom, J; Lidman, T; Vafaee, F (Algebraic & Geometric Topology, 2015-01-15)
      © 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 ...
    • Null surgery on knots in L-spaces 

      Ni, Y; Vafaee, F
      Let $K$ be a knot in an L-space $Y$ with a Dehn surgery to a surface bundle over $S^1$. We prove that $K$ is rationally fibered, that is, the knot complement admits a fibration over $S^1$. As part of the proof, we show that ...
    • On L-space knots obtained from unknotting arcs in alternating diagrams 

      Donald, A; McCoy, D; Vafaee, F
      Let $D$ be a diagram of an alternating knot with unknotting number one. The branched double cover of $S^3$ branched over $D$ is an L-space obtained by half integral surgery on a knot $K_D$. We denote the set of all such ...
    • On the Knot Floer Homology of Twisted Torus Knots 

      Vafaee, F (International Mathematics Research Notices, 2015)
      © 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 ...
    • Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic 

      Vafaee, F (Topology and its Applications, 2015-04)
      © 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 prism manifold realization problem 

      Ballinger, W; Hsu, CCY; Mackey, W; Ni, YI; Ochse, T; Vafaee, F
      The spherical manifold realization problem asks which spherical three-manifolds arise from surgeries on knots in $S^3$. In recent years, the realization problem for C, T, O, and I-type spherical manifolds has been solved, ...