arXiv research

Extends fibering theorems for 3-manifolds.

Study Veech groups in fibered 3-manifolds, proving no parabolics for fibers.

Study Turaev-Viro invariants of Seifert fibered 3-manifolds, proving volume conjecture.

Unique incompressible surface in fibered 3-manifolds.

Describes 3-manifolds by families of singularly fibered surfaces.

Study connects surface projections in fibered 3-manifolds.

New bounds found for minimal surfaces in hyperbolic 3-manifolds.

Study shows certain subgroups of fibered 3-manifolds are convex cocompact.

The infimal Heegaard gradient of a compact 3-manifold was defined and studied by Marc Lackenby in an approach toward the well-known virtually Haken conjecture. As instructive examples, we consider Seifert fibered 3-manifolds, and show that a Seifert fibered 3-manifold has zero infimal Heegaard gradient if and only if i…

Study on fibered knots in 3-manifolds, proving unrelated volume and genus.

Finite quotients of fibered hyperbolic 3-manifold groups detect taut polynomials.

Paper connects homologically fibered links to solutions of equations.

Study fiber-preserving, orientation-reversing involutions on Seifert fibered 3-manifolds.

Dehn surgery on knots in 3-manifolds rarely results in surface fibered manifolds.

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

Proof of existence for ideal triangulations that normalize fibers in certain 3-manifolds.

Defines a new symplectic Khovanov homology for links in fibered 3-manifolds.

It is known that every closed oriented 3-manifold is homology cobordant to a hyperbolic 3-manifold. By contrast we show that many homology cobordism classes contain no Seifert fibered 3-manifold. This is accomplished by determining the isomorphism type of the rational cohomology ring of all Seifert fibered 3-manifolds …

Study Turaev-Viro invariants of 3-manifolds with toroidal boundary.

New example shows noncontractible fiberings for a 3-manifold.

Lower bounds for cover degrees of hyperbolic 3-manifolds.

Study flippable Heegaard splittings in Seifert fibered spaces.

In a series of papers the authors proved that twisted Alexander polynomials detect fibered 3-manifolds, and they showed that this implies that a closed 3-manifold N is fibered if and only if S^1 x N is symplectic. In this note we summarize some of the key ideas of the proofs. We also give new evidence to the conjecture…

The paper studies entropy in branched covers of 3-manifolds.

Prism complexes help classify 3-manifolds, especially Seifert fiber spaces.

We characterize the closed, oriented, Seifert fibered 3-manifolds which are oriented boundaries of Stein manifolds. We also show that for this class of 3-manifolds the existence of Stein fillings is equivalent to the existence of symplectic fillings.

Infinite family of hyperbolic 3-manifolds with large volumes.

Study uses twisted Alexander polynomials to link fibered classes in 3-manifolds.

Proves 3-manifold groups uniquely identify hyperbolic bundles.

We study principal curvatures of fibers and Heegaard surfaces smoothly embedded in hyperbolic 3-manifolds. It is well known that a fiber or a Heegaard surface in a hyperbolic 3-manifold cannot have principal curvatures everywhere less than one in absolute value. We show that given an upper bound on the genus of a minim…

It is known that the Alexander polynomial detects fibered knots and 3-manifolds that fiber over the circle. In this note, we show that when the Alexander polynomial becomes inconclusive, the notion of "knot adjacency", studied in the paper "Knot adjacency, genus and essential tori" by the authors, can be used to obtain…

New bases found for Kauffman bracket skein module of fibered torus.

Researchers prove a conjecture linking 1-loop invariants to torsion for fibered 3-manifolds.

Let $p$ be a prime. In this paper, we classify the geometric 3-manifolds whose fundamental groups are virtually residually $p$. Let $M=M^3$ be a virtually fibered 3-manifold. It is well-known that $G=π_1(M)$ is residually solvable and even residually finite solvable. We prove that $G$ is always virtually residually $p$…

The paper studies twisted signature invariants of fibered knots and 3-manifolds.

We verify that the rational blow-down schemes along certain Seifert fibered 3-manifolds found by the second author, Szabo and Wahl are, in fact, symplectic operations.

A classical result in knot theory says that the Alexander polynomial of a fibered knot is monic and that its degree equals twice the genus of the knot. This result has been generalized by various authors to twisted Alexander polynomials and fibered 3-manifolds. In this paper we show that the conditions on twisted Alexa…

New examples of hyperbolic 3-manifolds with unique profinite structure.

We classify positive, tight contact structures on closed Seifert fibered 3-manifolds with base S^2, three singular fibers and e_0\geq 0.

We determine the closed, oriented Seifert fibered 3-manifolds which carry positive tight contact structures. Our main tool is a new non-vanishing criterion for the contact Ozsvath-Szabo invariant.

In this paper it is proven that there is at most one way, up to isotopy, in which a connected, hyperbolic, orientable 3-manifold can fiber over the circle with monodromy in the Torelli group.

The paper introduces the spirality character of the almost fiber part for a closed essentially immersed subsurface of a closed orientable aspherical 3-manifold, which generalizes an invariant due to Rubinstein and Wang. The subsurface is virtually embedded if and only if the almost fiber part is aspiral, and in this ca…

We address the question: how common is it for a 3-manifold to fiber over the circle? One motivation for considering this is to give insight into the fairly inscrutable Virtual Fibration Conjecture. For the special class of 3-manifolds with tunnel number one, we provide compelling theoretical and experimental evidence t…

New Legendrian bounds for non-fibered knots in 3-manifolds.

Anosov flows found on many hyperbolic 3-manifolds.

In two previous papers the author presented a general construction of finite, fiber- and orientation-preserving group actions on orientable Seifert manifolds. In this paper we restrict our attention to elliptic 3-manifolds. A proof is given that orientation-reversing and fiber-preserving diffeomorphisms of Seifert mani…

We describe explicit horizontal open books on some Seifert fibered 3--manifolds. We show that the contact structures compatible with these horizontal open books are Stein fillable and horizontal as well. Moreover we draw surgery diagrams for some of these contact structures.

In 2007 Agol showed that if N is an aspherical compact 3-manifold with empty or toroidal boundary such that its fundamental group is virtually RFRS, then $N$ is virtually fibered. We give a largely self-contained proof of Agol's theorem using complexities of sutured manifolds.