arXiv research

Researchers determine the Thurston unit ball for a family of $n$-chained links and find conditions for fibered faces.

We study the connections between subsurface projections in curve and arc complexes in fibered 3-manifolds and Agol's veering triangulation. The main theme is that large-distance subsurfaces in fibers are associated to large simplicial regions in the veering triangulation, and this correspondence holds uniformly for all…

The Teichmueller polynomial of a fibered 3-manifold plays a useful role in the construction of mapping class having small stretch factor. We provide an algorithm that computes this polynomial of the fibered face associated to a pseudo-Anosov mapping class of a disc homeomorphism. As a byproduct, our algorithm allows us…

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…

New flows represent Thurston norm ball faces, differing by veering mutations.

The paper studies fibers of maps in totally nonnegative spaces.

Constructs examples of complex 3D shapes with specific properties.

A polynomial invariant for veering triangulations helps in understanding 3-manifold fibers.

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…

New triangulations encode flows with vanishing polynomial.

Minimal stretch factor for non-orientable surfaces is small.

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

Study pseudo-Anosov monodromies' lengths in 3-manifolds' arc complex.

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…

Compactifies semi-simple Lie groups to manifolds with corners.

Graph manifolds' Thurston norms are sums of linear functionals, and every such norm can be realized.

We exhibit a closed hyperbolic 3-manifold which satisfies a very strong form of Thurston's Virtual Fibration Conjecture. In particular, this manifold has finite covers which fiber over the circle in arbitrarily many ways. More precisely, it has a tower of finite covers where the number of fibered faces of the Thurston …

New proof shows how to find stable loops in 3-manifolds.

Real blow-up, including inhomogeneous versions, of boundary faces of a manifold (with corners) is an important tool for resolving singularities, degeneracies and competing notions of homogeneity. These constructions are shown to be particular cases of `generalized boundary blow-up' in which a new manifold and blow-down…

We discuss fibered commensurability of fibrations on a hyperbolic 3-manifold, a notion introduced by Calegari, Sun and Wang. We construct manifolds with non-symmetric but commensurable fibrations on the same fibered face. We also prove that if a given manifold M does not have any hidden symmetries, then M does not admi…

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

We consider a hyperbolic surface bundle over the circle with the smallest known volume among hyperbolic manifolds having 3 cusps, so called "the magic manifold". We compute the entropy function on the fiber face of the unit ball with respect to the Thurston norm, determine homology classes whose representatives are gen…

Study pseudo-Anosov monodromies in fibered 3-manifolds using asymptotic translation lengths.

Let $M$ be a closed hyperbolic 3-manifold with a fibered face $σ$ of the unit ball of the Thurston norm on $H_2(M)$. If $M$ satisfies a certain condition related to Agol's veering triangulations, we construct a taut branched surface in $M$ spanning $σ$. This partially answers a 1985 question of Oertel, and extends an e…

Formula for projecting geodesics in hyperbolic 3-manifolds, relating lengths to subsurface projections.

Paper describes links of mixed polynomials with specific properties.

In this paper, we show an approach to build deep learning algorithms for recognizing signals in distributed fiber optic monitoring and security systems for long perimeters. Synthesizing such detection algorithms poses a non-trivial research and development challenge, because these systems face stringent error (type I a…

For each pseudo-Anosov map $φ$ on surface $S$, we will associate it with a $\mathbb{Q}$-submodule of $\mathbb{R}$, denoted by $A(S,φ)$. $A(S,φ)$ is defined by an interaction between the Thurston norm and dilatation of pseudo-Anosov maps. We will develop a few nice properties of $A(S,φ)$ and give a few examples to show …

Let $δ_{g,n}$ be the minimal dilatation of pseudo-Anosovs defined on an orientable surface of genus $g$ with $n$ punctures. Tsai proved that for any fixed $g \ge 2$, the logarithm of the minimal dilatation $\log δ_{g,n}$ is on the order of $\frac{\log n}{n}$. The main result of this paper is that if $2g+1$ is relativel…

Develops a method for manifold learning with small sample size datasets.

In this note we explore a connection between finite covers of surfaces and the Teichmüller polynomial of a fibered face of a hyperbolic 3--manifold. We consider the action of a homological pseudo-Anosov homeomorphism $ψ$ on the homology groups of a class of finite abelian covers of a surface $Σ_{g,n}$. Eigenspaces of t…

A refined form of the `Folk Theorem' that a smooth action by a compact Lie group can be (canonically) resolved, by iterated blow up, to have unique isotropy type is proved in the context of manifolds with corners. This procedure is shown to capture the simultaneous resolution of all isotropy types in a `resolution stru…

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. …

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

The paper proves the existence of a unique circle packing on hyperbolic surfaces.

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

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

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.

Optimizes master faces for 2D and 3D face verification using evolutionary algorithms and neural networks.

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

New examples show not all homology fiber bundles are topological.

Study shows simplicial volume of certain fiber bundles is zero.

New exotic 4-manifolds found with fiber bundles.

Study of Seifert fibered spaces using surface complexes.

We construct two infinite families of knots each of which admits a Seifert fibered surgery with none of these surgeries coming from Dean's primitive/Seifert-fibered construction. This disproves a conjecture that all Seifert fibered surgeries arise from Dean's primitive/Seifert-fibered construction. The (-3,3,5)-pretzel…

Face recognition systems are vulnerable to composite face reconstruction attacks.

We show that a compact complex surface which fibers smoothly over a curve of genus >1 with fibers of genus >1 fibers holomorphically. We deduce an improvement of a result in [D Kotschick, Math. Research Letters, 5 (1998) 227-234], and a characterisation of fibered surfaces with zero signature.