arXiv research

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

Extends Seifert algorithm to 3-manifolds via surgery.

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

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

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…

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 flippable Heegaard splittings in Seifert fibered spaces.

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 …

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…

New method alters Seifert surfaces without compression.

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

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.

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.

Classifies surfaces of section for Seifert fibrations.

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…

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

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 skein modules and character varieties of Seifert manifolds.

CR singularities in 3-manifolds can be cancelled by an isotopy supported in an arbitrarily small neighborhood of a Seifert surface.

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.

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

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

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

We prove that the fundamental group of any Seifert 3-manifold is conjugacy separable. That is, conjugates may be distinguished in finite quotients or, equivalently, conjugacy classes are closed in the pro-finite topology.

Recognition of Seifert fibered spaces with boundary is computationally tractable.

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

It is not completely unreasonable to expect that a computable function bounding the number of Pachner moves needed to change any triangulation of a given 3-manifold into any other triangulation of the same 3-manifold exists. In this paper we describe a procedure yielding an explicit formula for such a function if the 3…

I give a formula for computing the number of regular $Γ$-coverings of closed orientable Seifert 3-manifolds, for a given finite group $Γ$. The number is computed using a 3d TQFT with finite gauge group, through a cut-and-glue process.

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.

Method calculates $\mathbb{Z}_2$-Thurston norm for Seifert 3-manifolds using pseudo-horizontal surfaces.

The closed 3-manifolds of constant positive curvature were classified long ago by Seifert and Threlfall. Using well-known information about the orthogonal group O(4), we calculate their full isometry groups Isom(M), determine which elliptic 3-manifolds admit Seifert fiberings that are invariant under all isometries, an…

The path integral for the partition function of Chern-Simons gauge theory with a compact gauge group is evaluated on a general Seifert 3-manifold. This extends previous results and relies on abelianisation, a background field method and local application of the Kawasaki Index theorem.

Proves left-orderability of certain Dehn fillings on 3-manifolds.

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 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…

Quantum invariants of 3-manifolds linked to splice diagrams.

We compute a recently introduced geometric invariant of stricly pseudoconvex CR 3-manifolds for certain circle invariant spherical CR structures on Seifert manifolds. We give applications to the problem of filling the CR manifold by a complex hyperbolic manifold, and more generally by a Kaehler-Einstein or an Einstein …

Study monodromy relations in Seifert fibered spaces for 3-manifold fillings.

Study shows Seifert fibered spaces don't bound rational homology balls.

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…

We report on recent results of the authors concerning calculations of quantum invariants of Seifert 3-manifolds. These results include a derivation of the Reshetikhin-Turaev invariants of all oriented Seifert manifolds associated with an arbitrary complex finite dimensional simple Lie algebra, and a determination of th…

The Heegaard genus g of an irreducible closed orientable 3-manifold puts a limit on the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of the manifold by its canonical tori. For example, if p of the complementary components are not Seifert fibered, then p < g. This result gene…

The Ozsvath-Szabo contact invariant is a complete classification invariant for tight contact structures on small Seifert fibered 3-manifolds which are L-spaces.

We calculate the RT-invariants of all oriented Seifert manifolds directly from surgery presentations. We work in the general framework of an arbitrary modular category as in [V. G. Turaev, Quantum invariants of knots and 3--manifolds, de Gruyter Stud. Math. 18, Walter de Gruyter (1994)], and the invariants are expresse…

Study shows partial hyperbolicity leads to Anosov dynamics in 3-manifolds.

This paper shows that the Seifert volume of each closed non-trivial graph manifold is virtually positive. As a consequence, for each closed orientable prime 3-manifold $N$, the set of mapping degrees $cD(M,N)$ is finite for any 3-manifold $M$, unless $N$ is finitely covered by either a torus bundle, or a trivial circle…