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 “right-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.
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…
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 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.
We give a sufficient condition using the Ozsváth-Stipsicz-Szabó concordance invariant Upsilon for the monodromy of the open book decomposition of a fibered knot to be right-veering. As an application, we generalize a result of Baker on ribbon concordances between fibered knots. Following Baker, we conclude that either …
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 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 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…
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…
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 …
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.
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 …
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_…
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.
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.
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.
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…
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…
The authors introduce Morse foliated open books for studying contact manifolds.
problem Studying contact manifolds with boundary.
method Introducing Morse foliated open books and extending the right-veering concept.
result Right-veering plays a similar role in detecting overtwistedness in foliated open books.
We discuss how the fractional Dehn twist coefficient behaves under a fully ramified branched covering of an open book, and give applications to both topological and contact 3-manifolds. Among them, we show that non-right-veering closed braids represent virtually loose transverse links.
In this paper we provide the classification of tight contact structures on some small Seifert fibered manifolds. As an application of this classification, combined with work of Lekili in \cite{L2010}, we obtain infinitely many counterexamples to a question of Honda-Kazez-Matić that asks whether a right-veering, non-des…
Positive braids linked to knot invariants and geometric monodromy groups.
problem Understanding knot invariants and geometric monodromy groups for positive braids.
method Associate braid monodromy groups to positive braids, identify these groups with framed mapping class groups for knots, and use these to determine knot invariants.
result Geometric monodromy groups of irreducible singularities are determined by genus and Arf invariant of associated knots.
Quandles and Monodromymath.GT
We show that a variety of monodromy phenomena arising in geometric topology and algebraic geometry are most conveniently described in terms of quandle homomorphisms from a knot quandle associated to the base to a quandle associated to a fiber. We consider the cases of the monodromy of a branched covering, braid monodro…
Paper studies Lagrangian submanifolds and their homological monodromy.
problem Understanding the homological monodromy of Lagrangian submanifolds.
method Proves triviality of homological Lagrangian monodromy under specific conditions.
result Homological Lagrangian monodromy is trivial if Hofer energy is less than minimum energy of J-holomorphic spheres and discs.
New conditions found for hyperbolic bicycle tracks.
problem Conditions for hyperbolic bicycle tracks.
method Hyperbolic development interpretation of bicycling monodromy.
result New necessary and sufficient conditions for hyperbolic bicycle tracks.
Noninjective monodromy found in polynomial critical point tracking.
problem Tracking critical points in polynomials leads to noninjective monodromy.
method Monic squarefree complex polynomials with prescribed critical point multiplicities.
result Monodromy map is noninjective for polynomials with exactly two critical points.
Arithmeticity of the Kontsevich--Zorich monodromies of certain families of square-tiled surfacesmath.DS
The study finds arithmetic groups often in square-tiled surface monodromies.
problem Understanding arithmetic properties of square-tiled surfaces.
method Analyzing variations of Hodge structures and Kontsevich-Zorich monodromies.
result Arithmetic groups are frequent in low genus square-tiled surfaces.
Characterizes conical angles for metrics with dihedral symmetry.
problem Understanding metrics with specific symmetry properties.
method Using recent results on local invariants of quadratic differentials.
result Complete characterization of conical angles for dihedral spherical metrics.
The geometric monodromy of a plane curve singularity is a quasi-finite diffeomorphism. In this paper we locate the reduction curves of the geometric monodromy and the quadratic vanishing cycles of the singularity. An application to the geometric monodromy group is given.
For any topological groupoid G and any homomorphism from a locally compact Hausdorff topological group K to G, we construct an associated monodromy group. We prove that Morita equivalent topological groupoids have the same monodromy groups. We show how the monodromy groups can be used to test if a Lie groupoid lacks fa…
Study of monodromy and vanishing cycles for complete intersection curves.
problem Computing topological monodromy of complete intersection curves.
method Innovative tools for studying monodromy of tensor products of very ample line bundles, induction on multi-degree.
result Answer given by the r-spin mapping class group associated to the maximal root of the adjoint line bundle.
In this work we describe a method to reconstruct the braid monodromy of the preimage of a curve by a Kummer cover. This method is interesting, since it combines two techniques, namely, the reconstruction of a highly non-generic braid monodromy with a systematic method to go from a non-generic to a generic braid monodro…
The paper studies the index of a specific monodromy for origamis in a particular stratum.
problem Determining the index of a Kontsevich-Zorich monodromy for origamis in .
method Analyzing the action of the Veech group on the non-tautological part of the homology.
result The index of the Kontsevich-Zorich monodromy is either 1 or 3 for origamis in .
Polynomials with distinct critical values have braid monodromy groups equal to braid groups.
problem Understanding the structure of braid monodromy groups of polynomials.
method Analyzing the critical values of polynomials to determine their braid monodromy groups.
result The braid monodromy group of a polynomial equals the braid group if the polynomial has distinct critical values.
The monodromy conjecture states that every pole of the topological (or related) zeta function induces an eigenvalue of monodromy. This conjecture has already been studied a lot; however, in full generality it is proven only for zeta functions associated to a polynomial in two variables. In this article we consider zeta…
We consider spaces of plane curves in the setting of algebraic geometry and of singularity theory. On one hand there are the complete linear systems, on the other we consider unfolding spaces of bivariate polynomials of Brieskorn-Pham type. For suitable open subspaces we can define the bifurcation braid monodromy takin…
Arithmetic Kontsevich-Zorich monodromy found in a specific origami surface.
problem Exploring the monodromy of a symmetric origami in genus 4.
method Analyzing the Veech group and symplectic group properties of the origami.
result Existence of arithmetic Kontsevich-Zorich monodromy in a specific origami.
Holomorphic connections found on Riemann surfaces with Fuchsian monodromy.
problem Existence of holomorphic connections with Fuchsian monodromy on Riemann surfaces.
method Construction of compact Riemann surfaces with specific holomorphic vector bundles and connections.
result Existence of holomorphic connections with maximal Euler class and Fuchsian monodromy.
We outline the construction of the holonomy groupoid of a locally Lie groupoid and the monodromy groupoid of a Lie groupoid. These specialise to the well known holonomy and monodromy groupoids of a foliation, when the groupoid is just an equivalence relation.
Study shows hyperbolic knots' monodromy without fixed points.
problem Understanding fixed points in knot monodromy.
method Using Baldwin--Hu--Sivek argument and knot Floer homology.
result Monodromy of hyperbolic fibered knots is freely isotopic to a map with no fixed points.
This work classifies monodromy in vineyards using singularity theory.
problem Understanding and predicting monodromy in vineyards for topological data analysis.
method Using a connection with singularity theory, the study classifies monodromy in vineyards of 1-manifolds in R^2.
result Monodromy in vineyards occurs only if they contain a specific singularity of the distance function.
This paper generalizes monodromy maps for projective structures with poles.
problem Understanding the monodromy of projective structures with poles.
method Generalizing the monodromy map from compact curves to those with poles.
result The monodromy map for projective structures with poles is a local biholomorphism.
In this paper we consider completed coverings that are branched coverings in the sense of Fox. For completed coverings between PL manifolds we give a characterization of the existence of a monodromy representation and the existence of a locally compact monodromy representation. These results stem from a characterizatio…
Monodromy map from differential systems to character variety is generically immersive for complex -representations.
problem Characterizing when the monodromy map is immersive for differential systems.
method Analyzing the space of -differential systems on a compact Riemann surface and the character variety of -representations.
result The monodromy map is an immersion at the generic point when the complex dimension of is at least three.