Browsing by Author "0906019"
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(1,1) Lspace knots
Vafaee, Faramarz; Greene, Joshua Evan; Lewallen, Sam (COMPOSITIO MATHEMATICA, 20180501)We characterize the (1, 1) knots in the threesphere and lens spaces that admit nontrivial Lspace surgeries. As a corollary, 1bridge braids in these manifolds admit non trivial Lspace surgeries. We also recover ... 
A slicing obstruction from the $\frac {10}{8}$ theorem
Vafaee, Faramarz; Donald, Andrew (Proceedings of the American Mathematical Society, 20160829)© 2016 American Mathematical Society. From Furuta’s 10/8 theorem, we derive a smooth slicing obstruction for knots in S3 using a spin 4manifold whose boundary is 0surgery on a knot. We show that this obstruction is able ... 
Berge–Gabai knots and L–space satellite operations
Vafaee, Faramarz; Hom, Jennifer; Lidman, Tye (Algebraic & Geometric Topology, 20150115)© 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 Lspaces
Vafaee, Faramarz; Ni, YiLet $K$ be a knot in an Lspace $Y$ 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 Lspace knots obtained from unknotting arcs in alternating diagrams
Vafaee, Faramarz; Donald, Andrew; McCoy, DuncanLet $D$ be a diagram of an alternating knot with unknotting number one. The branched double cover of $S^3$ branched over $D$ is an Lspace 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, Faramarz (International Mathematics Research Notices, 2015)© 2014 The Author(s) 2014. Published by Oxford University Press. All rights reserved. For permissions, please email: journals.permissions@oup.com. In this paper, we study the knot Floer homology of a subfamily of twisted ... 
On the Stein framing number of a knot
Vafaee, Faramarz; Mark, Thomas E; Piccirillo, LisaFor an integer $n$, write $X_n(K)$ for the 4manifold obtained by attaching a 2handle to the 4ball along the knot $K\subset S^3$ with framing $n$. It is known that if $n< \overline{\text{tb}}(K)$, then $X_n(K)$ admits ... 
Seifert surfaces distinguished by sutured Floer homology but not its Euler characteristic
Vafaee, Faramarz (Topology and its Applications, 201504)© 2015 Elsevier B.V. In this paper we find a family of knots with trivial Alexander polynomial, and construct two nonisotopic Seifert surfaces for each member in our family. In order to distinguish the surfaces we study ... 
The prism manifold realization problem
Vafaee, Faramarz; Ballinger, William; Hsu, Chloe ChingYun; Mackey, Wyatt; Ni, Yi; Ochse, TynanThe spherical manifold realization problem asks which spherical threemanifolds arise from surgeries on knots in $S^3$. In recent years, the realization problem for C, T, O, and Itype spherical manifolds has been solved, ... 
The prism manifold realization problem II
Vafaee, Faramarz; Ballinger, William; Ni, Yi; Ochse, TynanWe continue our study of the realization problem for prism manifolds. Every prism manifold can be parametrized by a pair of relatively prime integers $p>1$ and $q$. We determine a complete list of prism manifolds $P(p, q)$ ... 
The prism manifold realization problem III
Vafaee, Faramarz; Ballinger, William; Ni, Yi; Ochse, TynanEvery prism manifold can be parametrized by a pair of relatively prime integers $p>1$ and $q$. In our earlier papers, we determined a complete list of prism manifolds $P(p, q)$ that can be realized by positive integral ...