Steven Boyer
YOU?
Author Swipe
View article: Slope detection, taut foliations, and the relative L-space conjecture
Slope detection, taut foliations, and the relative L-space conjecture Open
The $L$-space conjecture asserts the equivalence, for prime $3$-manifolds, of three properties: not being an $L$-space ($NLS$), having a left-orderable fundamental group ($LO$), and admitting a co-orientable taut foliation ($CTF$). In this…
View article: Order-detection of slopes on the boundaries of knot manifolds
Order-detection of slopes on the boundaries of knot manifolds Open
Motivated by the L-space conjecture, we investigate various notions of order-detection of slopes on knot manifolds. These notions are designed to characterise when rational homology 3-spheres, obtained by gluing compact manifolds along tor…
View article: Cyclic branched covers of Seifert links and properties related to the $ADE$ link conjecture
Cyclic branched covers of Seifert links and properties related to the $ADE$ link conjecture Open
In this article we show that all cyclic branched covers of a Seifert link have left-orderable fundamental groups, and therefore admit co-oriented taut foliations and are not $L$-spaces, if and only if it is not an $ADE$ link up to orientat…
View article: JSJ decompositions of knot exteriors, Dehn surgery and the $L$-space conjecture
JSJ decompositions of knot exteriors, Dehn surgery and the $L$-space conjecture Open
In this article, we apply slope detection techniques to study properties of toroidal $3$-manifolds obtained by performing Dehn surgeries on satellite knots in the context of the $L$-space conjecture. We show that if $K$ is an $L$-space kno…
View article: Recalibrating $\mathbb{R}$-order trees and $\mbox{Homeo}_+(S^1)$-representations of link groups
Recalibrating $\mathbb{R}$-order trees and $\mbox{Homeo}_+(S^1)$-representations of link groups Open
In this paper we study the left-orderability of $3$-manifold groups using an enhancement, called recalibration, of Calegari and Dunfield's "flipping" construction, used for modifying $\mbox{Homeo}_+(S^1)$-representations of the fundamental…
View article: Order-detection of slopes on the boundaries of knot manifolds
Order-detection of slopes on the boundaries of knot manifolds Open
Motivated by the L-space conjecture, we investigate various notions of order-detection of slopes on knot manifolds. These notions are designed to characterise when rational homology 3-spheres obtained by gluing compact manifolds along toru…
View article: Slope detection and toroidal 3-manifolds
Slope detection and toroidal 3-manifolds Open
The $L$-space conjecture asserts the equivalence, for prime 3-manifolds, of three properties: not being an $L$-space, having a left-orderable fundamental group, and admitting a co-oriented taut foliation. We investigate these properties fo…
View article: Dehn fillings of knot manifolds containing essential twice-punctured tori
Dehn fillings of knot manifolds containing essential twice-punctured tori Open
We show that if a hyperbolic knot manifold $M$ contains an essential twice-punctured torus $F$ with boundary slope $β$ and admits a filling with slope $α$ producing a Seifert fibred space, then the distance between the slopes $α$ and $β$ i…
View article: On the Tits alternative for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mi mathvariant="italic">PD</mml:mi><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math> groups
On the Tits alternative for groups Open
We prove the Tits alternative for an almost coherent group which is not virtually properly locally cyclic. In particular, we show that an almost coherent group which cannot be generated by less than four elements always contains a rank 2…
View article: Taut foliations in branched cyclic covers and left-orderable groups
Taut foliations in branched cyclic covers and left-orderable groups Open
We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred knots in integer homology-spheres and cyclic…
View article: On definite strongly quasipositive links and L-space branched covers
On definite strongly quasipositive links and L-space branched covers Open
We investigate the problem of characterising the family of strongly quasipositive links which have definite symmetrised Seifert forms and apply our results to the problem of determining when such a link can have an L-space cyclic branched …
View article: On definite strongly quasipositive links and L-space branched covers
On definite strongly quasipositive links and L-space branched covers Open
We investigate the problem of characterising the family of strongly quasipositive links which have definite symmetrised Seifert forms and apply our results to the problem of determining when such a link can have an L-space cyclic branched …
View article: Taut foliations in branched cyclic covers and left-orderable groups
Taut foliations in branched cyclic covers and left-orderable groups Open
We study the left-orderability of the fundamental groups of cyclic branched covers of links which admit co-oriented taut foliations. In particular we do this for cyclic branched covers of fibred knots in integer homology $3$-spheres and cy…
View article: On the Tits altenative for $PD(3)$ groups
On the Tits altenative for $PD(3)$ groups Open
We prove the Tits alternative for an almost coherent $PD(3)$ group which is not virtually properly locally cyclic. In particular, we show that an almost coherent $PD(3)$ group which cannot be generated by fewer than four elements always co…
View article: Foliations, orders, representations, L-spaces and graph manifolds
Foliations, orders, representations, L-spaces and graph manifolds Open
View article: Knot complements, hidden symmetries and reflection orbifolds
Knot complements, hidden symmetries and reflection orbifolds Open
In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the -sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic re…
View article: 1-domination of knots
1-domination of knots Open
We say that a knot $k_1$ in the $3$-sphere {\it $1$-dominates} another $k_2$ if there is a proper degree 1 map $E(k_1) \to E(k_2)$ between their exteriors, and write $k_1 \ge k_2$. When $k_1 \ge k_2$ but $k_1 \ne k_2$ we write $k_1 > k_2$.…
View article: Slope detection, foliations in graph manifolds, and L-spaces
Slope detection, foliations in graph manifolds, and L-spaces Open
A graph manifold rational homology $3$-sphere $W$ with a left-orderable fundamental group admits a co-oriented taut foliation, though it is unknown whether it admits a smooth co-oriented taut foliation. In this paper we extend the gluing t…
View article: Graph manifold ℤ-homology 3-spheres and taut foliations
Graph manifold ℤ-homology 3-spheres and taut foliations Open
We show that a graph manifold which is a Z-homology 3-sphere not homeomorphic to either S3 or Σ(2, 3, 5) admits a horizontal foliation. This combines with known results to show that the conditions of not being an L-space, of having a left-…
View article: Knot complements, hidden symmetries and reflection orbifolds
Knot complements, hidden symmetries and reflection orbifolds Open
In this article we examine the conjecture of Neumann and Reid that the only hyperbolic knots in the $3$-sphere which admit hidden symmetries are the figure-eight knot and the two dodecahedral knots. Knots whose complements cover hyperbolic…