New knot found with unique property.
problem Existence of hyperbolic fibered slice knots with specific monodromy.
method Constructed a specific type of hyperbolic fibered slice knot.
result Negative answer to a question posed by Hubbard et al.
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48 results for “veering monodromy”
Floer homology detects right-veering monodromy in fibered knots.
problem Detecting right-veering monodromy in fibered knots.
method Using Heegaard Floer homology and symplectic Floer homology.
result Knot Floer homology characterizes tight contact structures.
The study examines exceptional surgeries on hyperbolic fibered knots and their properties.
problem Understanding the bounds and characterizing slopes of surgeries on hyperbolic fibered knots.
method Analyzes the monodromy of knots and their surgeries, using properties of fibered knots and Seifert fibered spaces.
result Proves bounds on slopes of surgeries and characterizes certain knots.
Certain fibered hyperbolic 3-manifolds admit a , which can be constructed algorithmically given the stable lamination of the monodromy. These triangulations were introduced by Agol in 2011, and have been further studied by several others in the years since. We obtain exper…
A closed braid naturally gives rise to a transverse link in the standard contact 3-space. We study the effect of the dynamical properties of the braid monodromy, such as right-veering, on the contact-topological properties of the transverse link and its transverse invariants in knot Floer and Khovanov homologies. In pa…
A divide on an orientable 2-orbifold gives rise to a fibration of the unit tangent bundle to the orbifold.We characterize the corresponding monodromies as exactly the products of a left-veering horizontal and a right-veering vertical antitwist with respect to a cylinder decomposition, where the notion of an antitwist i…
The paper extends monodromy theory to incompressible surfaces in 3-manifolds and applies it to link primeness.
problem Primeness of incompressible surfaces and links in 3-manifolds.
method Develops monodromies for incompressible surfaces, introduces right-veeringness, and applies these to link primeness.
result Strongly quasipositive surfaces are right-veering, and a new characterization of right-veering surfaces is provided.
We prove that any mapping class on a compact oriented surface with nonempty boundary can be made pseudo-Anosov and right-veering after a sequence of positive stabilizations.
The Upsilon invariant helps classify fibered knots and their open book decompositions.
problem Classifying fibered knots and their open book decompositions.
method Using the Ozsváth-Stipsicz-Szabó concordance invariant Upsilon.
result Fibered knots satisfying a specific condition are either unique in their smooth concordance classes or provide counterexamples to the Slice-Ribbon Conjecture.
We introduce an essential open book foliation, a refinement of the open book foliation, and develop technical estimates of the fractional Dehn twist coefficient (FDTC) of monodromies and the FDTC for closed braids, which we introduce as well. As applications, we quantitatively study the `gap' of overtwisted contact str…
We study diffeomorphisms of compact, oriented surfaces, developing methods of distinguishing those which have positive factorizations into Dehn twists from those which satisfy the weaker condition of right veering. We use these to construct open book decompositions of Stein-fillable 3-manifolds whose monodromies have n…
We present an alternate description of the Ozsvath-Szabo contact class in Heegaard Floer homology. Using our contact class, we prove that if a contact structure (M,ξ) has an adapted open book decomposition whose page S is a once-punctured torus, then the monodromy is right-veering if and only if the contact structure i…
The study computes invariants of satellite knots using bordered Floer homology.
problem Computing invariants of satellite knots with specific patterns.
method Using bordered Floer homology and the immersed curve interpretation of the bordered pairing theorem.
result Satellites with thin fibered companions or specific patterns have thin knot Floer homology.
Study contact structures on four-punctured spheres, finding infinitely many overtwisted monodromies.
problem Understanding contact structures on four-punctured spheres.
method Combining techniques from Ito-Kawamuro and Min-Varvarezos, analyzing overtwisted and reducible monodromies.
result Classification of reducible monodromies with non-zero Heegaard Floer invariant.
In this paper, we focus on contact structures supported by planar open book decompositions. We study right-veering diffeomorphisms to keep track of overtwistedness property of contact structures under some monodromy changes. As an application we give infinitely many examples of overtwisted contact structures supported …
New polynomial helps compute flow growth rates in 3D manifolds.
problem Computing growth rates of pseudo-Anosov flows in 3-manifolds.
method Modified veering polynomial and combinatorial flow graph.
result Computes growth rates of pseudo-Anosov flows after cutting.
Finite quotients of fibered hyperbolic 3-manifold groups detect taut polynomials.
problem Detecting taut polynomials of fibered faces of Thurston norm balls
method Developing a framework for profinite invariance of twisted multivariable Alexander polynomials
result Proving finite quotients detect taut polynomials
Detects right-veering properties in open books using combinatorial methods.
problem Determining the right-veering property of contact structures.
method Combinatorial approach to detect left-veering arcs in open books.
result Existence of an algorithm to detect right-veering for compact surfaces.
Developed algorithms to compute three polynomial invariants of veering triangulations.
problem Computing polynomial invariants of veering triangulations.
method Introduced and used algorithms for taut, veering, and Teichmüller polynomials based on upper and lower tracks of veering triangulations.
result Proved that the lower and upper taut polynomials are equal but the veering polynomials can differ.
New method connects veering triangulations to dynamic pairs.
problem Understanding veering triangulations and their properties.
method Shearing decomposition of veering triangulations.
result Canonically associated dynamic pairs of branched surfaces.
Veering branched surfaces help construct geodesic flows on curved surfaces.
problem Constructing geodesic flows on negatively curved surfaces.
method Introduce veering branched surfaces and surgeries, then use them to construct veering triangulations that correspond to geodesic flows.
result Explicit constructions of veering branched surfaces corresponding to geodesic flows on negatively curved surfaces.
Agol recently introduced the concept of a veering taut triangulation, which is a taut triangulation with some extra combinatorial structure. We define the weaker notion of a "veering triangulation" and use it to show that all veering triangulations admit strict angle structures. We also answer a question of Agol, givin…
New triangulations encode flows with vanishing polynomial.
problem Constructing veering triangulations with vanishing taut polynomial.
method Using connections between veering triangulations and pseudo-Anosov flows.
result Created arbitrarily large veering triangulations with vanishing taut polynomial.
We introduce a notion of "quasi-right-veering" for closed braids, which plays an analogous role to "right-veering" for open books. We show that a transverse link in a contact 3-manifold is non-loose if and only if every braid representative of with respect to every open book decomposition that supports …
Veering triangulations link Thurston norm and isotopy of surfaces.
problem Understanding the relationship between Thurston norm and isotopy of surfaces.
method Analyzing veering triangulations and their relation to Thurston norm and isotopy.
result Veering triangulations specify faces of Thurston norm balls and link isotopy of surfaces.
Legendrian arcs connect veering triangulations to Anosov flows.
problem Connecting veering triangulations to Anosov flows for study.
method Realizing edges as Legendrian arcs with a bicontact structure.
result Veering triangulations can be placed in steady position.
Dynamics of veering triangulations: infinitesimal components of their flow graphs and applicationsmath.GT
Study on veering triangulations and their flow graphs, proving new applications.
problem Understanding the structure of veering triangulations and their flow graphs.
method Analyzing the infinitesimal components of the flow graph associated with veering triangulations.
result Infinitesimal components of veering triangulations' flow graphs have specific forms related to subsets called 'walls'.
Characterizing right-veering homeomorphisms of the punctured torus via the Burau representationmath.GT
We classify right-veering homeomorphisms of the once-punctured torus using the Burau representation of the 3-strand braid group. We show that reducible and periodic mapping classes in B_3 can be identified as right-veering by consideration of the reduced version of the Burau representation. Given any element beta in B_…
New loom spaces link flows and triangulations.
problem Understanding flows and triangulations in 3D.
method Introducing loom spaces and proving associated triangulations.
result Locally veering triangulations can be associated to loom spaces.
New method shows how certain groups act on 3-orbifolds.
problem Understanding how groups act on 3-dimensional spaces.
method Using veering pairs of laminations and loom spaces.
result Groups with invariant veering pairs are hyperbolic 3-orbifold groups.
We introduce twist left-veering mapping classes of punctured surfaces. We prove that a twist left-veering open book supports an overtwisted contact structure and determine when the closed braid coming from the punctures is loose or virtually loose.
This paper is the third in a sequence establishing a dictionary between the combinatorics of veering triangulations equipped with appropriate filling slopes, and the dynamics of pseudo-Anosov flows (without perfect fits) on closed three-manifolds. Our motivation comes from the work of Agol and Guéritaud. Agol introduce…
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…
Mutations and faces of the Thurston norm ball dynamically represented by multiple distinct flowsmath.GT
New flows represent Thurston norm ball faces, differing by veering mutations.
problem Dynamic representation of Thurston norm ball faces by distinct flows.
method Combining veering triangulations and mutations to represent faces by multiple flows.
result Non-fibered faces can be represented by two distinct flows differing by veering mutations.
Recently, Ian Agol introduced a class of "veering" ideal triangulations for mapping tori of pseudo-Anosov homeomorphisms of surfaces punctured along the singular points. These triangulations have very special combinatorial properties, and Agol asked if these are "geometric", i.e. realised in the complete hyperbolic met…
Agol recently introduced the notion of a veering triangulation, and showed that such triangulations naturally arise as layered triangulations of fibered hyperbolic 3-manifolds. We prove, by a constructive argument, that every veering triangulation admits positive angle structures, recovering a result of Hodgson, Rubins…
A polynomial invariant for veering triangulations helps in understanding 3-manifold fibers.
problem Understanding the fibers of 3-manifolds using veering triangulations.
method Introducing a polynomial invariant associated to veering triangulations and using flow graphs.
result The invariant recovers the Teichmüller polynomial for fibered faces and determines cones in homology.
New method finds unique branched surfaces in 3-manifolds.
problem Finding unique branched surfaces in 3-manifolds.
method Proving endperiodic maps have periodic splitting sequences.
result Veering branched surfaces are unique up to equivalence.
New train tracks for complex homeomorphisms found.
problem Existence of irreducible train tracks for pseudo-Anosov homeomorphisms.
method Starting from a veering triangulation, identify and modify branches to bypass obstructions.
result Construction of invariant train tracks with irreducible transition matrix.
We exhibit infinitely many overtwisted, right-veering, non-destabilizable open books, thus providing infinitely many counterexamples to a conjecture of Honda-Kazez-Matic. The page of all our open books is a four-holed sphere and the underlying 3-manifolds are lens spaces.
We give an alternative proof of a theorem of Honda-Kazez-Matić that every non-right-veering open book supports an overtwisted contact structure. We also study two types of examples that show how overtwisted discs are embedded relative to right-veering open books.
The taut polynomial equals a twisted Alexander polynomial.
problem Understanding the relationship between taut polynomials and Alexander polynomials.
method Defined taut polynomial of veering triangulations and proved it equals a twisted Alexander polynomial.
result The taut polynomial equals a twisted Alexander polynomial of the underlying manifold.
We initiate the study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary. The monoid strictly contains the monoid of products of positive Dehn twists. We explain the relationship to tight contact structures and open book decompositions.
Finitely many pseudo-Anosov flows without perfect fits in a 3-manifold.
problem Finite number of pseudo-Anosov flows without perfect fits in a 3-manifold.
method Analysis of veering triangulations and pseudo-Anosov flows.
result Finiteness of pseudo-Anosov flows without perfect fits.
We continue our study of the monoid of right-veering diffeomorphisms on a compact oriented surface with nonempty boundary, introduced in [HKM2]. We conduct a detailed study of the case when the surface is a punctured torus; in particular, we exhibit the difference between the monoid of right-veering diffeomorphisms and…
Let be a closed hyperbolic 3-manifold with a fibered face of the unit ball of the Thurston norm on . If satisfies a certain condition related to Agol's veering triangulations, we construct a taut branched surface in spanning . This partially answers a 1985 question of Oertel, and extends an e…
We prove the existence of foliations transverse to pseudo-Anosov flows using veering triangulations.
problem Existence of foliations transverse to pseudo-Anosov flows in 3-manifolds.
method Combinatorial approach via veering triangulations and branched surfaces.
result Existence of transverse foliations for certain pseudo-Anosov flows.
We study an explicit construction of planar open books with four binding components on any three-manifold which is given by integral surgery on three component pure braid closures. This construction is general, indeed any planar open book with four binding components is given this way. Using this construction and resul…