arXiv research

This paper completes proofs for left orderable slopes of double twist knots.

The paper studies slopes for knot fillings with left-orderable fundamental groups.

Study slopes on knot manifolds to understand their fundamental groups.

A rational number $r$ is called a left orderable slope of a knot $K \subset S^3$ if the 3-manifold obtained from $S^3$ by $r$-surgery along $K$ has left orderable fundamental group. In this paper we consider the double twist knots $C(k,l)$ in the Conway notation. For any positive integers $m$ and $n$, we show that if $…

New property helps show many knot fillings are not left-orderable.

Detect slopes in toroidal 3-manifolds to prove properties of fundamental groups.

The Euler class of taut foliations on Dehn fillings is studied, leading to new left-orderable slopes.

We show that the resulting manifold by $r$-surgery on a large class of two-bridge knots has left-orderable fundamental group if the slope $r$ satisfies certain conditions. This result gives a supporting evidence to a conjecture of Boyer, Gordon and Watson that relates $L$-spaces and the left-orderability of their funda…

Paper tackles $L$-space conjecture for knot manifolds, proving equivalence for some properties.

We show that the properties of admitting a co-oriented taut foliation and having a left-orderable fundamental group are equivalent for rational homology $3$-sphere graph manifolds and relate them to the property of not being a Heegaard-Floer L-space. This is accomplished in several steps. First we show how to detect fa…

For any hyperbolic twist knot in the 3-sphere, we show that the resulting manifold by $r$-surgery on the knot has left-orderable fundamental group if the slope $r$ satisfies the inequality $0\le r \le 4$.

We show that the resulting manifold by $r$-surgery on the knot $5_2$, which is the two-bridge knot corresponding to the rational number 3/7, has left-orderable fundamental group if the slope $r$ satisfies $0\le r\le 4$.

For any hyperbolic genus one 2-bridge knot in the 3-sphere, we show that the resulting manifold by $r$-surgery on the knot has left-orderable fundamental group if the slope $r$ lies in some range which depends on the knot.

The paper proves left-orderability for certain Dehn fillings of pseudo-Anosov mapping tori.

In this paper, we prove that the fundamental group of the manifold obtained by Dehn surgery along a $(-2,3,2s+1)$-pretzel knot ($s\ge 3$) with slope $\frac{p}{q}$ is not left orderable if $\frac{p}{q}\ge 2s+3$, and that it is left orderable if $\frac{p}{q}$ is in a neighborhood of zero depending on $s$.

New method detects left-orderable surgeries on knot 6_2.

We show that the resulting manifold by $r$-surgery on the hyperbolic twist knot $K_m, \, m \ge 2$, has left-orderable fundamental group if the slope $r$ satisfies the condition $r \in (-4,2m)$ if $m$ is even, and $r \in [0,4] \cup (\frac{4m}ω+4, 2m+4)$ if $m$ is odd, where $ω>1$ is the unique real solution of the equat…

The paper extends techniques to create non-left-orderable manifolds from links with multiple boundary components.

The study explores knots and manifolds, proving properties and non-left-orderable groups.

We construct a 1-parameter family of $\mathrm{SL}_2(\mathbf{R})$ representations of the pretzel knot $P(-2,3,7)$. As a consequence, we conclude that Dehn surgeries on this knot are left-orderable for all rational surgery slopes less than 6. Furthermore, we discuss a family of knots and exhibit similar orderability resu…

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 theorem of arXiv:1401.7726 to graph manifold rational homology solid tori and use …

Study of knot surgeries and JSJ decompositions to tackle $L$-space conjecture.

The paper constructs metrics with negative curvature on complex manifolds.

The paper enhances representations to show left-orderability of certain 3-manifold groups.

Develops slope detection for 3-manifolds with torus boundaries.

Characterizes slopes for Markov ordering on prime pairs.

Whitehead link surgeries are not L-spaces if they support taut foliations.

Paper proposes efficient algorithms for designing SLOPE penalty sequences.

No characterizing slopes for multi-component links.

The study examines exceptional surgeries on hyperbolic fibered knots and their properties.

Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.

Paper introduces mcTangent for real-time dynamical systems.

We study a family of sparse estimators defined as minimizers of some empirical Lipschitz loss function -- which include the hinge loss, the logistic loss and the quantile regression loss -- with a convex, sparse or group-sparse regularization. In particular, we consider the L1 norm on the coefficients, its sorted Slope…

Nested model averaging improves high-dimensional linear regression performance.

We consider a class of manifolds with torus boundary admitting bordered Heegaard Floer homology of a particularly simple form, namely, the type D structure may be described graphically by a disjoint union of loops. We develop a calculus for studying bordered invariants of this form and, in particular, provide a complet…

The study shows involutory quandles of certain links are not left-orderable.

The paper defines circular orderability for quandles and explores their properties.

A left order on a magma (e.g., semigroup) is a total order of its elements that is left invariant under the magma operation. A natural topology can be introduced on the set of all left orders of an arbitrary magma. We prove that this topological space is compact. Interesting examples of nonassociative magmas, whose spa…

Left orderability proven for certain 3-manifolds with specific foliations.

Let K be a knot in the 3--sphere. An r-surgery on K is left-orderable if the resulting 3--manifold K(r) of the surgery has left-orderable fundamental group, and an r-surgery on K is called an L-space surgery if K(r) is an L-space. A conjecture of Boyer, Gordon and Watson says that non-reducing surgeries on K can be cla…

Study uses satellite data to predict tailings dam collapse risk.

Motivated by recent activity in low-dimensional topology, we provide a new criterion for left-orderability of a group under the assumption that the group is circularly-orderable: A group $G$ is left-orderable if and only if $G \times \mathbb{Z}/n\mathbb{Z}$ is circularly-orderable for all $n > 1$. This implies that eve…

Study shows surgeries on certain knots yield left-orderable 3-manifolds.

Constructs foliations from manifold group left orders.

Proves left-orderability of mapping class groups of infinite-type surfaces.

There are various results that frame left-orderability of a group as a geometric property. Indeed, the fundamental group of a 3-manifold is left-orderable whenever the first Betti number is positive; in the case that the first Betti number is zero this property is closely tied to the existence of certain nice foliation…

Solves the Wiegold problem by showing free products of left-orderable groups have normal rank > 1.

New proof shows left orderability of 3-manifold groups with specific foliations.