15 citations · 82 across the 22 of their papers we have counts for
25 papers
The orientation-reversing minimal stretch factor problem in small genus
Pierre Dehornoy, Erwan Lanneau, Livio Liechti +1
We determine the minimal stretch factors among all orientation-reversing pseudo-Anosov mapping classes of the closed orientable surfaces of genus two, three and four.
Genus one Birkhoff sections for geodesic flows on orbifolds
Pierre Dehornoy
For a hyperbolic orientable 2-orbifold of genus with at most conic points, we prove that the geodesic flow on the unitary tangent bundle$\mathrm{T}^1\mathc…
Left-handed geodesic flow of spheres of revolution
Pierre Dehornoy, Ana Rechtman
A flow on a 3-manifold is left-handed if any two ergodic invariant measures have negative linking number. We prove that on a 2-sphere of revolution whose curvature is -pinched…
The cat-bat map, the figure-eight knot, and the five orbifolds
Pierre Dehornoy
These are expository notes in which we explain how one can see some exceptional surgeries connecting the suspension of the cat-bat map and the unit tangent bundles to some hyperbol…
Hopf Arborescent Links, Minor Theory, and Decidability of the Genus Defect
Pierre Dehornoy, Corentin Lunel, Arnaud de Mesmay
While the problem of computing the genus of a knot is now fairly well understood, no algorithm is known for its four-dimensional variants, both in the smooth and in the topological…
Generic properties of -dimensional Reeb flows: Birkhoff sections and entropy
Vincent Colin, Pierre Dehornoy, Umberto Hryniewicz +1
In this paper we use broken book decompositions to study Reeb flows on closed -manifolds. We show that if the Liouville measure of a nondegenerate contact form can be approximat…
Complex vs convex Morse functions and geodesic open books
Pierre Dehornoy, Burak Ozbagci
Suppose that is a closed and oriented surface equipped with a Riemannian metric. In the literature, there are three seemingly distinct constructions of open books on the unit (…
Minor theory for quasipositive surfaces
Sebastian Baader, Pierre Dehornoy, Livio Liechti
The set of quasipositive surfaces is closed under incompressible inclusion. We prove that the induced order on fibre surfaces of positive braid links is almost a well-quasi-order.…
On the existence of supporting broken book decompositions for contact forms in dimension 3
Vincent Colin, Pierre Dehornoy, Ana Rechtman
We prove that in dimension 3 every nondegenerate contact form is carried by a broken book decomposition. As an application we get that if M is a closed irreducible oriented 3-manif…
Divide monodromies and antitwists on surfaces
Pierre Dehornoy, Livio Liechti
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…
Almost equivalence of suspension Anosov flows
Mario Shannon, Pierre Dehornoy
We provide a written proof of a result due to H. Minakawa, which states that all suspension Anosov flows generated by hyperbolic matrices with positive trace are pairwise almost eq…
Vector fields and genus in dimension 3
Pierre Dehornoy, Ana Rechtman
Given a flow on a 3-dimensional integral homology sphere, we give a formula for the Euler characteristic of its transverse surfaces, in terms of boundary data only. We illustrate t…
The trunkenness of a volume-preserving vector field
Pierre Dehornoy, Ana Rechtman
We construct a new invariant-the trunkenness-for volume-perserving vector fields on S^3 up to volume-preserving diffeomorphism. We prove that the trunkenness is independent from th…
Intersection norms on surfaces and Birkhoff cross sections
Pierre Dehornoy, Marcos Cossarini
For every finite collection of curves on a surface, we define an associated (semi-)norm on the first homology group of the surface. The unit ball of the dual norm is the convex hul…
Signature and concordance of positive knots
Sebastian Baader, Pierre Dehornoy, Livio Liechti
We derive a linear estimate of the signature of positive knots, in terms of their genus. As an application, we show that every knot concordance class contains at most finitely many…
Which geodesic flows are left-handed ?
Pierre Dehornoy
We prove that the geodesic flow on the unit tangent bundle to a hyperbolic 2-orbifold is left-handed if and only if the orbifold is a sphere with three conic points. As a consequen…
Coding of geodesics and Lorenz-like templates for some geodesic flows
Pierre Dehornoy, Tali Pinsky
We construct a template with two ribbons that describes the topology of all periodic orbits of the geodesic flow on the unit tangent bundle to any sphere with three cone points wit…
Small dilatation homeomorphisms as monodromies of Lorenz knots
Pierre Dehornoy
We exhibit low-dilatation families of surface homeomorphisms among monodromies of Lorenz knots.
Trefoil Plumbing
Sebastian Baader, Pierre Dehornoy
We give a criterion for an open book to contain an n-times iterated Hopf plumbing summand. As an application, we show that fibre surfaces of positive braid knots admit a trefoil pl…
Almost commensurability of 3-dimensional Anosov flows
Pierre Dehornoy
Two flows are topologically almost commensurable if, up to removing finitely many periodic orbits and taking finite coverings, they are topologically equivalent. We prove that all…
Minor theory for surfaces and divides of maximal signature
Sebastian Baader, Pierre Dehornoy
The paper is partially withdrawn: in its current form, Lemma 2.3 is false, so that our proof of Theorem A and Proposition B has an important gap. We were unable to fix it yet. Any…
Genus one Birkhoff sections for geodesic flows
Pierre Dehornoy
We prove that the geodesic flow on the unit tangent bundle to every hyperbolic 2-orbifold that is a sphere with 3 or 4 singular points admits explicit genus one Birkhoff sections,…
Geodesic flow, left-handedness, and templates
Pierre Dehornoy
We establish that, for every hyperbolic orbifold of type (2, q, ) and for every orbifold of type (2, 3, 4g+2), the geodesic flow on the unit tangent bundle is left-handed.…
On the zeroes of the Alexander polynomial of a Lorenz knot
Pierre Dehornoy
We show that the zeroes of the Alexander polynomial of a Lorenz knot all lie in some annulus whose width depends explicitly on the genus and the braid index of the considered knot.