A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
New method connects veering triangulations to dynamic pairs.
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.
Developed algorithms to compute three polynomial invariants of veering triangulations.
Legendrian arcs connect veering triangulations to Anosov flows.
Study on veering triangulations and their flow graphs, proving new applications.
Veering triangulations link Thurston norm and isotopy of surfaces.
New loom spaces link flows and triangulations.
Veering branched surfaces help construct geodesic flows on curved surfaces.
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…
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…
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…
A polynomial invariant for veering triangulations helps in understanding 3-manifold fibers.
The taut polynomial equals a twisted Alexander polynomial.
New flows represent Thurston norm ball faces, differing by veering mutations.
Finitely many pseudo-Anosov flows without perfect fits in a 3-manifold.
New train tracks for complex homeomorphisms found.
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.
New 3D shapes found without certain flows.
Every pseudo-Anosov mapping class defines an associated veering triangulation of a punctured mapping torus. We show that generically, is not geometric. Here, the word "generic" can be taken either with respect to random walks in mapping class groups or with respect to counting geodesic…
New method finds unique branched surfaces in 3-manifolds.
Characterizes pseudo-Anosov orbit spaces via bifoliated planes
New method shows how certain groups act on 3-orbifolds.
New method constructs Birkhoff sections for pseudo-Anosov flows with controlled complexity.
Any hyperbolic surface bundle over the circle gives rise to a continuous surjection from the circle to the sphere, by work of Cannon and Thurston. We prove that the order in which this surjection fills out the sphere is dictated by a natural triangulation of the surface bundle (introduced by Agol) when all singularitie…
The study improves bounds on pseudo-Anosov maps and certifies minimum and accumulation points of normalized dilatations.
Characterizes transverse surfaces for pseudo-Anosov flows in 3-manifolds.
We show that the cone over a fibered face of a compact fibered hyperbolic 3-manifold is dual to the cone generated by the homology classes of finitely many curves called minimal stable loops living in the associated veering triangulation. We also present a new, more hands-on proof of Mosher's Transverse Surface Theorem…
New polynomial helps compute flow growth rates in 3D manifolds.
Detects right-veering properties in open books using combinatorial methods.
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 …
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_…
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.
New knot found with unique property.
Shows Anosov flows with genus one sections, supporting a conjecture.
Floer homology detects right-veering monodromy in fibered knots.
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…
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 study examines exceptional surgeries on hyperbolic fibered knots and their properties.
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 …
The authors introduce Morse foliated open books for studying contact manifolds.
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.