Related papers: Slope detection and toroidal 3-manifolds

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…

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…

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 torus…

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…

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 knot…

In this article, we construct infinitely many (small Seifert fibred, hyperbolic and toroidal) rational homology $3$-spheres that admit co-orientable taut foliations, but none with vanishing Euler class. In the context of the $L$-space…

For each connected alternating tangle, we provide an infinite family of non-left-orderable L-spaces. This gives further support for Conjecture [3] of Boyer, Gordon, and Watson that is a rational homology 3-sphere is an L-space if and only…

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…

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 prove that if $M$ is a rational homology sphere that is a Dehn surgery on the Whitehead link, then $M$ is not an $L$-space if and only if $M$ supports a coorientable taut foliation. The left orderability of some of these manifolds is…

We introduce the notion of a strong L-space, a closed, oriented rational homology 3-sphere whose Heegaard Floer homology can be determined at the chain level. We prove that the fundamental group of a strong L-space is not left-orderable.…

We study a class of 3-manifolds called strong L-spaces, which by definition admit a certain type of Heegaard diagram that is particularly simple from the perspective of Heegaard Floer homology. We provide evidence for the possibility that…

We show that a class of 3-manifolds with non left-orderable fundamental group are Heegaard Floer homology L-spaces

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…

Boyer, Gordon, and Watson have conjectured that an irreducible rational homology 3-sphere is an L-space if and only if its fundamental group is not left-orderable. Since Dehn surgeries on knots in $S^3$ can produce large families of…

We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…

We study positive braid knots (the knots in the three-sphere realized as positive braid closures) through the lens of the L-space conjecture. This conjecture predicts that if $K$ is a non-trivial positive braid knot, then for all $r <…

For an oriented irreducible 3-manifold M with non-empty toroidal boundary, we describe how sutured Floer homology ($SFH$) can be used to determine all fibered classes in $H^1(M)$. Furthermore, we show that the $SFH$ of a balanced sutured…

We describe a relationship between the monopole Floer homology of three-manifolds and the geometry of Riemann surfaces. Consider an automorphism $\varphi$ of a compact Riemann surface $\Sigma$ with quotient $\mathbb{P}^1$. There is a…