arXiv research

Study Kauffman bracket skein modules of Seifert fibered spaces.

The paper proves tight fibered knots are minimal in a specific knot order.

Investigates conditions for GKM fiber bundles and realizability of fiber bundles of GKM graphs.

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

Defines products for fibered corners manifolds, generalizing resolutions.

The paper proves Schauder estimates for Laplace-Beltrami on manifolds with fibered boundaries.

Given a null-cobordant oriented framed link $L$ in a closed oriented $3$--manifold $M$, we determine those links in $M \setminus L$ which can be realized as the singular point set of a generic map $M \to \mathbb{R}^2$ that has $L$ as an oriented framed regular fiber. Then, we study the linking behavior between the sing…

In early 1930s Seifert and Threlfall classified up to conjugacy the finite subgroups of $\mathrm{SO}(4)$, this gives an algebraic classification of orientable spherical 3-orbifolds. For the most part, spherical 3-orbifolds are Seifert fibered. The underlying topological space and singular set of non-fibered spherical 3…

In this paper we study kleinian groups of Schottky type whose limit set is a wild knot in the sense of Artin and Fox. We show that, if the ``original knot'' fibers over the circle then the wild knot $Λ$ also fibers over the circle. As a consequence, the universal covering of $\mathbb{S}^{3}-Λ$ is $\mathbb{R}^{3}$. We p…

New operations transform braids into P-fibered braids.

The volume spectrum of fiber bundles is bounded by the product of the base's volume spectrum and the fiber's volume.

In this survey, we remind some fibrations structure theorems (also called Milnor's fibrations) recently proved in the real and complex case, in the local and global settings. We give several Poincaré-Hopf type formulae which relates the Euler-Poincaré characteristic of these fibers (also called Milnor's fibers) and ind…

Anosov flows found on many hyperbolic 3-manifolds.

We prove that a Lefschetz fibration over the disc that, after compactification, has the same singular fibers as an extremal rational elliptic surface can be obtained by deleting a singular fiber and a section from the rational extremal elliptic surface, i.e. such a Lefschetz fibration is determined up to topological eq…

Constructs special Lagrangian submanifolds in Calabi-Yau 3-folds.

The paper studies the topology of hyperspaces of k-dimensional convex sets.

The study bounds and characterizes surfaces containing smooth conics and twistor fibers in a flag threefold.

Surjectivity of Cannon-Thurston map proven for metric graph bundles.

This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian reduction (including reduction by stages) for Lie group actions, but also classica…

We use the Birman-Ko-Lee presentation of the braid group to show that all closures of strongly quasipositive braids whose normal form contains a positive power of the dual Garside element $δ$ are fibered. We classify links which admit such a braid representative in geometric terms as boundaries of plumbings of positive…

Geometric framework for aligning fiber tracts across subjects.

We determine the rank of the fundamental group of those hyperbolic 3-manifolds fibering over the circle whose monodromy is a sufficiently high power of a pseudo-Anosov map. Moreover, we show that any two generating sets with minimal cardinality are Nielsen equivalent.

Introduces generalized principal bundles and connections, linking them to standard gauge theories.

Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. …

Classifies certain 3D knots with specific properties.

We study the asymptotic behavior of the asymptotic translation lengths on the curve complexes of pseudo-Anosov monodromies in a fibered cone of a fibered hyperbolic 3-manifold $M$ with $b_1(M) \geq 2$. For a sequence $(Σ_n, ψ_n)$ of fibers and monodromies in the fibered cone, we show that the asymptotic translation len…

Paper finds infinite pairs of fiber-type curves with same topology but different embeddings.

Extends Frohman and Rannard's result to Seifert fiber spaces with singular surfaces.

Maps between circle bundles are studied, proving fiber-preserving and finiteness results for mapping degrees.

A prism is the product space $Δ\times I$ where $Δ$ is a 2-simplex and $I$ is a closed interval. As an analogue of simplicial complexes, we introduce prism complexes and show that every compact $3$-manifold has a prism complex structure. We call a prism complex special if each interior horizontal edge lies in four prism…

Thurston's fibered face theory allows us to partition the set of pseudo-Anosov mapping classes on different compact oriented surfaces into subclasses with related dynamical behavior. This is done via a correspondence between the rational points on fibered faces in the first cohomology of a hyperbolic 3-manifold and the…

This paper studies how key tensor properties are inherited in subtensors of tensor train decompositions.

We give a slope equality for fibered surfaces whose general fiber is a smooth plane curve. As a corollary, we prove a "strong" Durfee-type inequality for isolated hypersurface surface singularities, which implies Durfee's strong conjecture for such singularities with non-negative topological Euler number of the excepti…

Given a projective hyperkahler manifold with a holomorphic Lagrangian fibration, we prove that hyperkahler metrics with volume of the torus fibers shrinking to zero collapse in the Gromov-Hausdorff sense (and smoothly away from the singular fibers) to a compact metric space which is a half-dimensional special Kahler ma…

We prove the smoothness of the L^2-analytic torsion form on some fiber bundles with non-compact fibers of positive Novikov-Shubin invariant. We do so by generalizing the arguments of Azzali-Goette-Schick to an appropriate Sobolev space, and proving that the Novikov-Shubin invariant remains positive in the Sobolev setti…

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

We study the local curvature estimates of long-time solutions to the normalized Kähler-Ricci flow on compact Kähler manifolds with semi-ample canonical line bundles. Using these estimates, we prove that on such a manifold, the set of singular fibers of the semi-ample fibration on which the Riemann curvature blows up at…

We study the relationship between fibered ribbon 1-knots and fibered ribbon 2-knots by studying fibered slice disks with handlebody fibers. We give a characterization of fibered homotopy-ribbon disks and give analogues of the Stallings twist for fibered disks and 2-knots. As an application, we produce infinite families…

Introduces Darboux-Lie derivative for fiber bundles.

This paper extends previous work on genus two fibrations by studying and resolving singular fibers.

The paper proves a precise SYZ conjecture for toric Calabi-Yau manifolds with singular fibers.

The paper proves non-existence of positive scalar curvature on certain fiber bundles.

Uniformly finite Cannon--Thurston fibers in most hyperbolic settings.

New examples show not all homology fiber bundles are topological.

New exotic 4-manifolds found with fiber bundles.

Study shows simplicial volume of certain fiber bundles is zero.

Randomized fiber projections enhance neural network accuracy.

Let $M^3$ be an oriented 3-manifold. We investigate when one of the fibers or a combination of fiber components, $F_{best}$, of a \emph{harmonic} map $f: M^3 \to S^1$ with Morse-type singularities delivers the Thurston norm $χ_-([F_{best}])$ of its homology class $[F_{best}] \in H_2(M^3; \Z)$. In particular, for a map …