arXiv research

Study reveals uniform spectral gaps for random hyperbolic surfaces with few cusps.

Paper establishes tight lower bounds for minimizing certain smooth and convex functions.

Paper introduces 'zippers' for constructing universal circles.

Associated to each material body $\mathcal{B}$ there exists a groupoid $Ω\left( \mathcal{B} \right)$ consisting of all the material isomorphisms connecting the points of $\mathcal{B}$. The uniformity character of $\mathcal{B}$ is reflected in the properties of $Ω\left( \mathcal{B} \right)$: $\mathcal{B}$ is uniform if,…

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

Paper studies a generalized mean field equation on closed Riemann surfaces.

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.

New tester outperforms existing ones in uniformity testing.

Uniform deviation bounds limit the difference between a model's expected loss and its loss on an empirical sample uniformly for all models in a learning problem. As such, they are a critical component to empirical risk minimization. In this paper, we provide a novel framework to obtain uniform deviation bounds for loss…

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…

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.

A groupoid $Ω\left( \mathcal{B} \right)$ called material groupoid is naturally associated to any simple body $\mathcal{B}$. The material distribution is introduced due to the (possible) lack of differentiability of the material groupoid. Thus, the inclusion of these new objects in the theory of material bodies opens th…

Study shows surgeries on specific links result in L-spaces.

The paper proves left-orderable surgeries for a specific type of knot.

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

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

Study proves non-left-orderability of 3-manifolds derived from specific knots.

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

Bi-orderable groups from left-orderable ones, showing non-profinite properties.

New conditions for circular orderability of direct products, linking to left-orderability of groups.

Study on left orderability of specific knot covers.

We show that a knot has a non left-orderable surgery if the knot group admits a generalized Baumslag-Solitar relator and satisfies certain conditions on a longitude of the knot. As an application, it is shown that certain positively twisted torus knots admit non left-orderable surgeries.

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

We prove that, among metrics on a compact quotient of $\left(\mathbb{H}^2\right)^n$ (product of hyperbolic planes) of prescribed total volume, the product of hyperbolic metrics has minimal volume entropy.

Study on pretzel knots and their left-orderable properties.

This paper investigates the geometry of compact contact manifolds that are uniformized by contact Lie groups, i.e., compact manifolds that are the quotient of some Lie group G with a left invariant contact structure and a uniform lattice subgroup. We re-examine Alexander's criteria for existence of lattices on solvable…

Proves left-orderability of certain Dehn fillings on 3-manifolds.

A $n$-dimensional Lie group $G$ equipped with a left invariant symplectic form $\om^+$ is called a symplectic Lie group. It is well-known that $\om^+$ induces a left invariant affine structure on $G$. Relatively to this affine structure we show that the left invariant Poisson tensor $π^+$ corresponding to $\om^+$ is po…

We show that the fundamental group of the $3$-manifold obtained by $\frac{p}{q}$-surgery along the $(n-2)$-twisted $(3,3m+2)$-torus knot, with $n,m \ge 1$, is not left-orderable if $\frac{p}{q} \ge 2n + 6m-3$ and is left-orderable if $\frac{p}{q}$ is sufficiently close to $0$.

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…

It is well known that a countable group admits a left-invariant total order if and only if it acts faithfully on R by orientation preserving homeomorphisms. Such group actions are special cases of group actions on simply connected 1-manifolds, or equivalently, actions on oriented order trees. We characterize a class of…

New description of $(1,1)$ L-space knots leads to non-left-orderable surgeries.

3-manifolds with Heegaard 2 admit taut foliations if their fundamental group is left-orderable.

Groups acting on bifoliated planes are left-orderable.

The paper finds infinite families of non-left-orderable L-spaces from tangles.

Study determines left-orderable properties of knot covers.

We show that certain negatively twisted torus knots admit Dehn surgeries yielding 3-manifolds with non left-orderable fundamental groups.

We show that the fundamental group of the double branched cover of an infinite family of homologically thin, non-quasi-alternating knots is not left-orderable, giving further support for a conjecture of Boyer, Gordon, and Watson that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental…

The paper introduces flat-topped PDFs for better fitting machine learning models.