50 citations · 405 across the 46 of their papers we have counts for
32 papers · 1 filter
Lens space surgeries on knots of small genus
Misha Schmalian, Steven Sivek
We prove that the pretzel knot is the only hyperbolic knot of genus at most with a lens space surgery. Our key technical result asserts that if a genus- hyperboli…
Ribbon concordance and fibered predecessors, II: the general case
John A. Baldwin, Jonathan Hanselman, Steven Sivek
The first and third authors recently proved that for each knot there are only finitely many hyperbolic fibered knots which are ribbon concordant to . In this pape…
Ribbon concordance and fibered predecessors
John A. Baldwin, Steven Sivek
Given any knot K in the 3-sphere, we prove that there are only finitely many hyperbolic fibered knots which are ribbon concordant to K. It follows that every fibered knot in the 3-…
Homology lens spaces and
Sudipta Ghosh, Steven Sivek, Raphael Zentner
We prove that if is a closed, oriented 3-manifold with first homology of order less than , then there is an irreducible representation $π_1(Y) \to \mathr…
Pseudo-Anosov flows on hyperbolic L-spaces
John A. Baldwin, Steven Sivek, Jonathan Zung
We prove that for each there is a hyperbolic L-space with pseudo-Anosov flows, no two of which are orbit equivalent. These flows have no perfect fits and are t…
L-spaces and knot traces
John A. Baldwin, Steven Sivek
There has been a great deal of interest in understanding which knots are characterized by which of their Dehn surgeries. We study a 4-dimensional version of this question: which kn…
Torus knots, the A-polynomial, and SL(2,C)
John A. Baldwin, Steven Sivek
The A-polynomial of a knot is defined in terms of SL(2,C) representations of the knot group, and encodes information about essential surfaces in the knot complement. In 2005, Dunfi…
Rational homology 3-spheres and SL(2,) representations
Sudipta Ghosh, Steven Sivek, Raphael Zentner
We use instanton gauge theory to prove that if is a closed, orientable -manifold such that is nontrivial and either -torsion or -torsion, and if $Y…
Small Heegaard genus and SU(2)
John A. Baldwin, Steven Sivek
Let be a closed, orientable 3-manifold with Heegaard genus 2. We prove that if has order , , or , then there is a representation $π_1(Y) \to \mathr…
Thurston norm and Euler classes of tight contact structures
Steven Sivek, Mehdi Yazdi
Bill Thurston proved that taut foliations of hyperbolic 3-manifolds have Euler classes of norm at most one, and conjectured that any integral second cohomology class of norm equal…
Zero-surgery characterizes infinitely many knots
John A. Baldwin, Steven Sivek
We prove that 0 is a characterizing slope for infinitely many knots, namely the genus-1 knots whose knot Floer homology is 2-dimensional in the top Alexander grading, which we clas…
An instanton take on some knot detection results
John A. Baldwin, Steven Sivek
We give new proofs that Khovanov homology detects the figure eight knot and the cinquefoils, and that HOMFLY homology detects and each of the pretzel knots. Fo…
Characterizing slopes for
John A. Baldwin, Steven Sivek
We prove that all rational slopes are characterizing for the knot , except possibly for positive integers. Along the way, we classify the Dehn surgeries on knots in that…
Floer homology and non-fibered knot detection
John A. Baldwin, Steven Sivek
We prove for the first time that knot Floer homology and Khovanov homology can detect non-fibered knots, and that HOMFLY homology detects infinitely many such knots; these theories…
Framed instanton homology and concordance, II
John A. Baldwin, Steven Sivek
We continue our study of the integer-valued knot invariants and , which together determine the dimensions of the framed instanton homologies of all nonzero De…
Floer homology and right-veering monodromy
John A. Baldwin, Yi Ni, Steven Sivek
We prove that the knot Floer complex of a fibered knot detects whether the monodromy of its fibration is right-veering. In particular, this leads to a purely knot Floer-theoretic c…
Small Dehn surgery and SU(2)
John A. Baldwin, Zhenkun Li, Steven Sivek +1
We prove that the fundamental group of 3-surgery on a nontrivial knot in the 3-sphere always admits an irreducible SU(2)-representation. This answers a question of Kronheimer and M…
Khovanov homology and the cinquefoil
John A. Baldwin, Ying Hu, Steven Sivek
We prove that Khovanov homology with coefficients in detects the torus knot. Our proof makes use of a wide range of deep tools in Floer homology, K…
Instanton L-spaces and splicing
John A. Baldwin, Steven Sivek
We prove that the 3-manifold obtained by gluing the complements of two nontrivial knots in homology 3-sphere instanton L-spaces, by a map which identifies meridians with Seifert lo…
Instanton Floer homology of almost-rational plumbings
Antonio Alfieri, John A. Baldwin, Irving Dai +1
We show that if is the boundary of an almost-rational plumbing, then the framed instanton Floer homology is isomorphic to the Heegaard Floer homology $\smash{…
Framed instanton homology and concordance
John A. Baldwin, Steven Sivek
We define two concordance invariants of knots using framed instanton homology. These invariants and provide bounds on slice genus and maximum self-linking num…
Surgery obstructions and character varieties
Steven Sivek, Raphael Zentner
We provide infinitely many rational homology 3-spheres with weight-one fundamental groups which do not arise from Dehn surgery on knots in . In contrast with previously known…
L-space knots are fibered and strongly quasipositive
John A. Baldwin, Steven Sivek
We give a new, conceptually simpler proof of the fact that knots in with positive L-space surgeries are fibered and strongly quasipositive. Our motivation for doing so is tha…
Instantons and L-space surgeries
John A. Baldwin, Steven Sivek
We prove that instanton L-space knots are fibered and strongly quasipositive. Our proof differs conceptually from proofs of the analogous result in Heegaard Floer homology, and inc…