arXiv research

The paper explores representations of graph manifolds to Seifert motion groups.

Extends Seifert algorithm to 3-manifolds via surgery.

Researchers calculate the volume of Seifert representations for graph manifolds and their covers.

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

We introduce and define "oriented framed measured lamination links" in a 3-manifold $M$. These generalize oriented framed links in 3-manifolds, and are confined to 2-dimensional improperly embedded subsurfaces of the 3-manifold. Just as some framed links bound Seifert surfaces, so also some framed lamination links boun…

3D topological order linked to Seifert manifolds and gauge groups.

Study on Seifert 4-manifolds to classify profinite rigidity.

Researchers compute knot invariants in Seifert manifolds using Wilson loops.

Classifies tight contact structures on specific Seifert fibered manifolds.

We study some properties of transverse contact structures on small Seifert manifolds, and we apply them to the classification of tight contact structures on a family of small Seifert manifolds.

In a paper published in 2002, the author gave a criterion to determine whether there is a fiber-preserving branched covering between two given orientable Seifert manifolds with orientable bases. Here we supply some details of the proof of two claims in that paper. We give an explicit construction of fiber-preserving br…

The paper characterizes symplectic fillings of Seifert 3-manifolds using rational blowdowns.

Classifies generalized Seifert fiber spaces and their branched covers.

Study flippable Heegaard splittings in Seifert fibered spaces.

Recognition of Seifert fibered spaces with boundary is computationally tractable.

New method alters Seifert surfaces without compression.

The paper defines a function for knots in Seifert manifolds and connects it to Witten-Reshetikhin-Turaev invariants.

Classifies surfaces of section for Seifert fibrations.

Study on Seifert fibered spherical 3-orbifolds, determining their unique fibrations.

Study on skein modules and character varieties of Seifert manifolds.

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…

A Seifert manifold is a 3-dimensional manifold with a circle action. It is a circle bundle (with singularities) over a 2-dimensional orbifold. In this note, we discuss a generalized Seifert manifolds. By definition, they have bundle-like structures whose fibers are infra- homogeneous spaces; that is, the fibers are fla…

We characterize the oriented Seifert-fibered three-manifolds which admit positive, transverse contact structures.

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

In this paper, it is shown that for any closed orientable $3$-manifold with positive simplicial volume, the growth of the Seifert volume of its finite covers is faster than the linear rate. In particular, each closed orientable $3$-manifold with positive simplicial volume has virtually positive Seifert volume. The resu…

The aim of this paper is to study Seifert bundle structures on simply connected 5--manifolds. We classify all such 5--manifolds which admit a Seifert bundle structure, and in a few cases all Seifert bundle structures are also classified. These results are then used to construct positive Ricci curvature Einstein metrics…

We define the surface complex for $3$-manifolds and embark on a case study in the arena of Seifert fibered spaces. The base orbifold of a Seifert fibered space captures some of the topology of the Seifert fibered space, so, not surprisingly, the surface complex of a Seifert fibered space always contains a subcomplex is…

Using contact surgery we define families of contact structures on certain Seifert fibered three-manifolds. We prove that all these contact structures are tight using contact Ozsath-Szabo invariants. We use these examples to show that, given a natural number n, there exists a Seifert fibered three-manifold carrying at l…

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

We derive a formula for the Dijkgraaf-Witten invariants of orientable Seifert 3-manifolds with orientable bases.

Character scheme of small Seifert 3-manifolds is reduced if and only if no exceptional abelian character exists.

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 …

We generalize H. Seifert's algorithm for finding a Seifert surface for a knot or link. The generalization applies to "framed oriented measured lamination links." For knots, a Seifert surface determines a unique framing. In our setting, we analyze the set of framed lamination links which bound Seifert laminations and ar…

The study sets constraints on 4-manifold forms linked to specific invariants.

Quantum invariants of 3-manifolds linked to splice diagrams.

We study small Seifert possibly chiral cosmetic surgeries on not necessarily null-homologous knot in rational homology spheres. Using $PSL_2(\mathbb{C})$-character variety theory we give a sharp bound on the number of slopes producing the same small Seifert manifold if the ambient manifold satisfies some representation…

The present paper gives an example of a rigid spherical cone-manifold and that of a flexible one which are both Seifert fibred.

In this paper, we investigate the minimal symplectic fillings of small Seifert 3-manifolds with a canonical contact structure. As a result, we classify all minimal symplectic fillings of small Seifert 3-manifolds satisfying certain conditions. Furthermore, we also demonstrate that every such a minimal symplectic fillin…

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.

In this article we classify up to isotopy tight contact structures on Seifert manifolds over the torus with one singular fibre.

We study the sutured Floer homology invariants of the sutured manifold obtained by cutting a knot complement along a Seifert surface, R. We show that these invariants are finer than the "top term" of the knot Floer homology, which they contain. In particular, we use sutured Floer homology to distinguish two non-isotopi…

We give an algorithm to find vertical essential tori in small Seifert fiber spaces with infinite fundamental groups. This implies that there are algorithms to decide whether a 3-manifold is a Seifert fiber space.

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.

Study on $Δ$ invariants of plumbed 3-manifolds, comparing with Heegaard-Floer homology.

Decides undecidability of equations and first-order theory for Seifert 3-manifold groups.

We use Heath's, Moriah's and Schultens's results to prove that irreducible Heegaard splittings of orientable Seifert manifolds with nonorientable base space are either vertical or horizontal.

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

Researchers compute Floer homotopy types and eta invariants for Seifert 3-manifolds.