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.
The paper studies pseudo-Anosov maps from typical Thurston constructions.
Survey on Thurston metric on Teichmüller space, focusing on extremal maps.
Constructs Teichmüller curve to study Thurston spine structure.
Two flexible, degenerate constructions related to Thurston's theorem.
New loxodromic elements found in infinite-type surfaces.
Computes minimal dilatation for Thurston maps on surfaces.
Constructs a universal Cannon-Thurston map for a new curve complex.
We show that the hyperbolic structure on a closed, orientable, hyperbolic 3-manifold can be constructed from a solution to the hyperbolic gluing equations using any triangulation with essential edges. The key ingredients in the proof are Thurston's spinning construction and a volume rigidity result attributed by Dunfie…
This paper extends Thurston and Tsuboi's work on foliations of .
In this paper, we present a new approach to the construction of Einstein metrics by a generalization of Thurston's Dehn filling. In particular in dimension 3, we will obtain an analytic proof of Thurston's result.
In 1974, Thurston proved that, up to isotopy, every automorphism of closed orientable surface is either periodic, reducible, or pseudo-Anosov. The latter case has lead to a rich theory with applications ranging from dynamical systems to low dimensional topology. Associated with every pseudo-Anosov map is a real number …
We define analogue of theta-functions on the Kodaira--Thurston manifold which is a compact 4-dimensional symplectic manifold and use them to construct canonical symplectic embedding of the Kodaira--Thurston manifold into the complex projective space (analogue of the Lefshetz theorem).
Construct pseudo-Anosovs from expanding interval maps, reconciling Thurston's construction.
We construct new explicit proper biharmonic functions on the -dimensional Thurston geometries $\Sol$, $\Nil$, $\SL2$, $H^2\times\rn$ and $S^2\times\rn$.
M. Kontsevich proposed a topological construction for an invariant Z of rational homology 3-spheres using configuration space integrals. G. Kuperberg and D. Thurston proved that Z is a universal real finite type invariant for integral homology spheres in the sense of Ohtsuki, Habiro and Goussarov. We review the Kontsev…
The Thurston spine's properties are studied in relation to Morse-Smale complexes.
We study Thurston's Lipschitz and curve metrics, as well as the arc metric on the Teichmueller space of one-hold tori equipped with complete hyperbolic metrics with boundary holonomy of fixed length. We construct natural Lipschitz maps between two surfaces equipped with such hyperbolic metrics that generalize Thurston'…
For any positive natural number we construct new explicit proper -harmonic functions on the celebrated -dimensional Thurston geometries $\Sol$, $\Nil$, $\SL2$, $\H^2\times\rn$ and $\s^2\times\rn$.
Constructs Anosov flows in hyperbolic 3-manifolds, disproving a conjecture.
If is an unramified covering map between two compact oriented surfaces of genus at least two, then it is proved that the embedding map, corresponding to , from the Teichmüller space , for , to actually extends to an embedding between the Thurston compactification of the tw…
The study finds all trace field degrees for Torelli group mappings.
In this paper we use Heegaard Floer link homology to determine the dual Thurston polytope for pretzel links of the form P(-2r_1-1, 2q_1, -2q_2, 2r_2+1) where r_i and q_i are positive integers. We apply this result to determine the Thurston norms of spanning surfaces for the individual link components, and we explicitly…
The paper compactifies stability conditions on curves, akin to Teichmüller theory.
Survey of Thurston norm properties and connections to 3-manifold invariants.
In this paper we study Thurston's automaton on the braid groups via binary operations. These binary operations are obtained from the construction of this automaton. We study these operations and find some connections between them in a "skew lattice" spirit.
New maps connect universal circles to ideal sphere for hyperbolic manifolds.
We introduce the notion of manifolds of amalgamation geometry and its generalization, split geometry. We show that the limit set of any surface group of split geometry is locally connected, by constructing a natural Cannon-Thurston map.
Bonahon's method for compactifying Teichmüller space extended to non-compact surfaces.
Constructs graph manifolds with many Anosov flows.
New method calculates Thurston norm for 3-manifolds with toroidal boundaries.
New Einstein metrics found on complex manifolds.
We find a constructive bound for the word length of a generating set for the centralizer of an element of the Mapping Class Group. As a consequence, we show that it is algorithmically decidable whether two postcritically finite branched coverings of the sphere are Thurston equivalent.
Invariants for 3-manifolds with toral boundaries, related by sutured decompositions.
Let be an infinite geodesically complete hyperbolic surface which can be decomposed into geodesic pairs of pants. We introduce Thurston's boundary to the Teichmüller space of the surface using the length spectrum analogous to Thurston's construction for finite surfaces. Thurston's boundary using the leng…
The study constructs AdS manifolds from Gromov-Thurston manifolds.
In this paper we prove that the limit set of any Weil-Petersson geodesic ray with uniquely ergodic ending lamination is a single point in the Thurston compactification of Teichmüller space. On the other hand, we construct examples of Weil-Petersson geodesics with minimal nonuniquely ergodic ending laminations and limit…
Paper computes hyperbolic structure of Borromean rings complement.
This paper uses combinatorial Ricci flow to tackle Thurston's triangulation conjecture.
In 1976, Thurston proved that taut foliations on closed hyperbolic 3-manifolds have Euler class of norm at most one, and conjectured that conversely, any integral second cohomology class with norm equal to one is the Euler class of a taut foliation. This is the first from a series of two papers that together give a neg…
In the Teichmüller space of a hyperbolic surface of finite type, we construct geodesic lines for Thurston's asymmetric metric having the property that when they are traversed in the reverse direction, they are also geodesic lines (up to reparametrization). The lines we construct are special stretch lines in the sense o…
In this note we discuss the behavior of the Gromov boundaries and limit sets for the surface subgroups of the mapping class group with accidental parabolics constructed by the author and A. Reid in earlier work. Specifically, we show that generically there are no Cannon--Thurston maps from the Gromov boundary to Thurst…
The study provides a criterion to compute the total Thurston-Bennequin invariant of Legendrian graphs.
We simplify Thurston norm computation for 2-bridge link complements.
Milnor-Thurston homology theory is a construction of homology theory that is based on measures. It is known that it is equivalent to singular homology theory in case of manifolds and complexes. Its behaviour for non-tame spaces is still unknown. This paper provides results in this direction. We prove that Milnor-Thurst…
About a decade ago Thurston proved that a vast collection of 3-manifolds carry metrics of constant negative curvature. These manifolds are thus elements of {\em hyperbolic geometry}, as natural as Euclid's regular polyhedra. For a closed manifold, Mostow rigidity assures that a hyperbolic structure is unique when it ex…
We define the Thurston-Bennequin polytope of a two-component link as the convex hull of all pairs of integers that arise as framings of a Legendrian representative. The main result of this paper is a description of the Thurston-Bennequin polytope for two-bridge links. As an application, we construct non-quasipositive s…
The paper proves inequalities linking geometric norms and Thurston norms in hyperbolic 3-manifolds.
We give a method for constructing a Legendrian representative of a knot in which realizes its maximal Thurston-Bennequin number under a certain condition. The method utilizes Stein handle decompositions of , and the resulting Legendrian representative is often very complicated (relative to the complexity of …