Related papers: Left orderability and taut foliations with one-sid…

Let $M_1$ and $M_2$ be knot manifolds and $M=M_1\cup_f M_2$ be the closed 3-manifold obtained by gluing up $M_1$ and $M_2$ via $f:\partial M_1\xrightarrow{\cong} \partial M_2$. We show that if $M$ admits a co-oriented taut foliation, then…

Examples suggest that there is a correspondence between L-spaces and 3-manifolds whose fundamental groups cannot be left-ordered. In this paper we establish the equivalence of these conditions for several large classes of such manifolds. In…

We show that any co-orientable foliation of dimension two on a closed orientable $3$-manifold with continuous tangent plane field can be $C^0$-approximated by both positive and negative contact structures unless all the leaves are simply…

We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation…

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.…

After a short summary of known results on surface-complexity of closed 3-manifolds, we will classify all closed orientable 3-manifolds with surface-complexity one.

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…

This paper explores the conjecture that the following are equivalent for rational homology 3-spheres: having left-orderable fundamental group, having non-minimal Heegaard Floer homology, and admitting a co-orientable taut foliation. In…

We classify all closed non-orientable $\mathbb{P}^2$-irreducible 3-manifolds obtained by identifying the faces of a cube. These turn out to be the closed non-orientable $\mathbb{P}^2$-irreducible 3-manifolds with surface-complexity one. We…

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…

This paper gives necessary and sufficient conditions on a compact, connected, orientable 3-manifold M for it to contain a knot K such that M-K is irreducible and pi_1(M) embeds in pi_1(M-K). This result provides counterexamples to a…

We show that for a taut foliation F with one-sided branching of an atoroidal 3-manifold M, one can construct a pair of genuine laminations with solid torus complementary regions which bind every leaf of F in a geodesic lamination. These…

We show that every irreducible toroidal integer homology sphere graph manifold has a left-orderable fundamental group. This is established by way of a specialization of a result due to Bludov and Glass for the almagamated products that…

For a riemannian foliation $\mathcal{F}$ on a closed manifold $M$, it is known that $\mathcal{F}$ is taut (i.e. the leaves are minimal submanifolds) if and only if the (tautness) class defined by the mean curvature form $\kappa_\mu$…

A 3-manifold is foliar if it supports a codimension-one co-oriented taut foliation. Suppose $M$ is an oriented 3-manifold with connected boundary a torus, and suppose $M$ contains a properly embedded, compact, oriented, surface $R$ with a…

In a recent paper Y. Hu has given a sufficient condition for the fundamental group of the r-th cyclic branched covering of S^3 along a prime knot to be left-orderable in terms of representations of the knot group. Applying her criterion to…

We call a closed, connected, orientable manifold in one of the categories TOP, PL or DIFF chiral if it does not admit an orientation-reversing automorphism and amphicheiral otherwise. Moreover, we call a manifold strongly chiral if it does…

Let $Y$ be a closed, connected, orientable three-manifold admitting a genus one open book decomposition with one boundary component. We prove that if $Y$ is an L-space, then the fundamental group of $Y$ is not left-orderable. This answers a…

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…

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation…