We provide an infinite family of left-ordered groups, all of which have a positive cone that is finitely generated as a semigroup. This family includes the Klein bottle group and the braid group B_3.
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48 results for “left-ordered central extensions”
Paper finds conditions for free product of circularly-ordered groups to have a circular ordering.
problem Conditions for free product of circularly-ordered groups to admit a circular ordering.
method Established a categorical framework to amalgamate left-ordered central extensions, applying work of Bludov and Glass.
result Necessary and sufficient conditions for the free product with amalgamation of circularly-ordered groups to admit a circular ordering.
Proves HNN extensions of nilpotent groups are left-orderable, constructs non-left-orderable examples.
problem Characterizing left-orderability in HNN extensions of groups.
method Analyzes HNN extensions of torsion-free nilpotent groups and left-orderable groups.
result Constructs examples of non-left-orderable HNN extensions of left-orderable groups.
The paper develops a method to construct left-orders on homology spheres from Dehn fillings.
problem Left-orderability of homology spheres obtained by Dehn filling.
method Holonomy extension loci of rational homology solid tori to study left-orderability.
result Intervals of Dehn fillings with left-orderable fundamental group.
Proves left-orderability of certain Dehn fillings on 3-manifolds.
problem Left-orderability of Dehn fillings on 3-manifolds.
method Constructing arcs of representations and using holonomy extension techniques.
result Establishes intervals of orderable Dehn fillings for odd pretzel knots.
Detect slopes in toroidal 3-manifolds to prove properties of fundamental groups.
problem Prove properties of fundamental groups of toroidal 3-manifolds.
method Slope detection using left-orders, foliations, and Heegaard Floer homology.
result Toroidal integer homology spheres have left-orderable fundamental groups.
The study shows involutory quandles of certain links are not left-orderable.
problem Determining left-orderability of involutory quandles of links.
method Using a non-left-orderability criterion for involutory quandles of non-split links, the study improved previous results and introduced new families of links.
result The involutory quandles of non-trivial alternating links and certain augmented alternating links are not left-orderable.
Study shows certain knots can be surgically altered to create non-left-orderable 3-manifolds.
problem Understanding non-left-orderable fundamental groups in 3-manifolds.
method Analyzing surgeries on negatively twisted torus knots.
result Certain knots can be surgically altered to create 3-manifolds with non-left-orderable fundamental groups.
Left orderability proven for certain 3-manifolds with specific foliations.
problem Proving left orderability for specific 3-manifolds with taut foliations.
method Analyzing the fundamental group of a 3-manifold with a co-orientable taut foliation.
result The fundamental group of the 3-manifold is left orderable.
New criterion links circular-orderability to left-orderability.
problem Understanding when circularly-orderable groups are left-orderable.
method Introducing a criterion based on the product of a group with integers.
result Groups are left-orderable if their product with integers is circularly-orderable.
Study shows surgeries on certain knots result in non-left-orderable 3-manifold groups.
problem Understanding when surgeries on knots result in non-left-orderable fundamental groups.
method Analyzing fundamental groups of 3-manifolds obtained by surgeries on specific knots.
result Fundamental groups are not left-orderable under certain conditions on surgery parameters.
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 shows surgeries on certain knots yield left-orderable 3-manifolds.
problem Integral Dehn surgeries on genus one fibered knots in lens spaces.
method Classification of genus one fibered knots by Baker and analysis of surgeries.
result All integral Dehn surgeries on these knots yield left-orderable 3-manifolds.
The paper finds left orderable slopes for specific double twist knots.
problem Identifying left orderable slopes for double twist knots.
method Analyzing the fundamental group of 3-manifolds obtained by surgery on double twist knots.
result Explicit intervals of rational numbers are left orderable slopes for certain double twist knots.
Motivated by conjectures relating group orderability, Floer homology, and taut foliations, we discuss a systematic and broadly applicable technique for constructing left-orders on the fundamental groups of rational homology 3-spheres. Specifically, for a compact 3-manifold with torus boundary, we give several crite…
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…
Foliations from left ordersmath.GT
Constructs foliations from manifold group left orders.
problem Creating foliations from group structures.
method Inputting a left order of a manifold's fundamental group produces a foliation.
result Establishes connections to 3D problems.
Solves the Wiegold problem by showing free products of left-orderable groups have normal rank > 1.
problem Wiegold problem about groups of normal rank > 1
method Topological argument and intricate construction of left-orders
result Free products of nontrivial left-orderable groups have normal rank > 1
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…
This paper completes proofs for left orderable slopes of double twist knots.
problem Proving the left orderability of slopes for double twist knots.
method Continuous families of hyperbolic SL2(R) representations of knot groups.
result Any slope in (-4n, 4m) is a left orderable slope of C(2m+1, -2n).
The paper proves left-orderable surgeries for a specific type of knot.
problem Existence of left-orderable Dehn surgeries on a specific knot.
method Cohomological criterion applied to two-bridge knots.
result Proves left-orderable Dehn surgeries for the two-bridge knots.
New method detects left-orderable surgeries on knot 6_2.
problem Detecting left-orderable fundamental groups of Dehn surgeries on knots.
method Using hyperbolic -representations.
result All Dehn surgeries on knot 6_2 with specified slopes have left-orderable fundamental groups.
Study proves non-left-orderability of 3-manifolds derived from specific knots.
problem Proving non-left-orderability of knot groups in 3-manifolds.
method Analyzing fundamental groups of cyclic branched covers of pretzel knots.
result Non-left-orderability of fundamental groups of -fold cyclic branched covers of for all integers and .
The paper studies slopes for knot fillings with left-orderable fundamental groups.
problem Understanding slopes for knot fillings with left-orderable fundamental groups.
method Using the Riley polynomial and root analysis, the paper computes and conjectures on slopes.
result The paper computes the range of rational slope for left-orderable fillings of two-bridge knots.
Proves left-orderability of mapping class groups of infinite-type surfaces.
problem Left-orderability of mapping class groups of infinite-type surfaces.
method Inductive construction of a stable Alexander system and ideal arc systems.
result Proves left-orderability using carefully chosen exhaustion by finite-type subsurfaces.
New findings on L-spaces and left-orderability for specific knot covers.
problem Understanding L-spaces and left-orderability in knot theory.
method Analyzing 3-fold and 5-fold cyclic branched covers of two-bridge knots.
result Fundamental groups of certain knot covers are not left-orderable.
Study on left orderability of specific knot covers.
problem Determining left orderability of knot covers.
method Computing nonabelian SL2(C) character varieties and analyzing real points.
result Left orderability of fundamental groups of cyclic branched covers.
New property helps show many knot fillings are not left-orderable.
problem Non-left-orderability of knot groups after Dehn filling.
method Introducing conjugate-slope property to study knot groups.
result The conjugate-slope property implies non-left-orderability of many knot fillings.
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 proof shows left orderability of 3-manifold groups with specific foliations.
problem Left orderability of 3-manifold groups with co-orientable taut foliations.
method Analyzes co-orientable taut foliations with orderable cataclysm to prove left orderability of 3-manifold fundamental groups.
result Proves left orderability of 3-manifold groups with specific foliations.
Study on pretzel knots and their left-orderable properties.
problem Investigating left-orderability of 3-manifolds derived from pretzel knots.
method Continuous paths of elliptic SL2(R) representations.
result Left-orderable fundamental groups for specific surgeries and branched covers.
The paper extends techniques to create non-left-orderable manifolds from links with multiple boundary components.
problem Creating infinite families of non-left-orderable manifolds from Dehn fillings.
method Order-detection of slopes to generalize techniques for multiple boundary components.
result Produces an infinite family of non-left-orderable Dehn fillings for hyperbolic links, including the Whitehead link.
Study shows surgeries on specific links result in L-spaces.
problem Understanding surgeries on specific links and their outcomes.
method Proving surgeries on chainmail links yield L-spaces using alternating surgeries.
result Alternating surgeries on chainmail links result in total L-spaces.
Study shows non-left-orderable surgeries for specific L-space knots.
problem Understanding left-orderability of surgeries on L-space knots.
method Analyzing L-space twisted torus knots and their surgeries.
result Fundamental groups of certain surgeries are not left-orderable.
We show that the resulting manifold by -surgery on a large class of two-bridge knots has left-orderable fundamental group if the slope satisfies certain conditions. This result gives a supporting evidence to a conjecture of Boyer, Gordon and Watson that relates -spaces and the left-orderability of their funda…
The paper examines surgeries on a specific type of knot and determines when the resulting manifold's fundamental group is left orderable.
problem Determining when the fundamental group of a Dehn surgery manifold on a specific knot is left orderable.
method Analyzes the fundamental group of manifolds obtained by Dehn surgery on -pretzel knots.
result The fundamental group of the manifold obtained by Dehn surgery along a -pretzel knot () with slope is not left orderable if , and left orderable if is in a neighborhood of zero depending on .
New description of L-space knots leads to non-left-orderable surgeries.
problem Characterizing and understanding L-space knots.
method Analyzing coherent reduced -diagrams to describe L-space knots and proving non-left-orderable fundamental groups.
result Any L-space obtained by Dehn surgery on a -knot in has a non-left-orderable fundamental group.
3-manifolds with Heegaard 2 admit taut foliations if their fundamental group is left-orderable.
problem Characterizing 3-manifolds with taut foliations.
method Proving existence of taut foliations based on left-orderability of the fundamental group.
result 3-manifolds with Heegaard genus 2 and left-orderable fundamental group admit co-orientable taut foliations.
The paper finds infinite families of non-left-orderable L-spaces from tangles.
problem Understanding the relationship between L-spaces and left-orderability.
method Using Dehn fillings of double branched covers of alternating tangles.
result Provides infinite families of non-left-orderable L-spaces.
Study determines left-orderable properties of knot covers.
problem Determining left-orderability of knot covers.
method Analyzing 2-bridge knots, including double-twist knots, using cyclic branched covers.
result Identifies specific integers for left-orderability of knot covers.
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…
We show that a class of 3-manifolds with non left-orderable fundamental group are Heegaard Floer homology L-spaces
We study the question of when cyclic branched covers of knots admit taut foliations, have left-orderable fundamental group, and are not L-spaces.
New method constructs actions on R capturing foliations, proving left-orderability.
problem Left-orderability of 3-manifold fundamental groups.
method Constructs actions of π1(M) on R, capturing foliations.
result Proves left-orderability of fundamental groups of 3-manifolds.
On -bridge braids, satellite knots, the manifold and non-left-orderable surgeries and fillingsmath.GT
The study explores knots and manifolds, proving properties and non-left-orderable groups.
problem Properties of knots and manifolds after surgeries and fillings.
method Fixed point method and Dehn surgery.
result Fundamental groups of certain manifolds are not left orderable.
Motivated by Clay and Watson's question on left-orderability of the fundamental group of the resultant space of an -surgery on the -cable knots for , this paper proves by elementary means that for specific pairs of -cable knots of torus knots, gives a surgery yi…
Bi-orderability and generalized torsion elements from the perspective of profinite propertiesmath.GR
Bi-orderable groups from left-orderable ones, showing non-profinite properties.
problem Non-profinite properties in bi-orderability and generalized torsion elements.
method Using fiber products to construct bi-orderable groups, showing non-profinite properties.
result Bi-orderability and generalized torsion elements are not profinite properties.
The paper constructs paths of SL2(R) representations for pretzel knots and shows left-orderability conditions.
problem Left-orderability of knot surgery manifolds.
method Explicit construction of continuous paths of SL2(R) representations.
result Fundamental groups of certain knot surgeries are left-orderable.