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.
Simplicial sets deformation retract onto transverse simplices.
We prove that transversal non-simplicity is preserved under taking connect sum, generalizing Vertesi's result.
The main result of this paper is a negative answer to the question: are all transversal knot types transversally simple? An explicit infinite family of examples is given of closed 3-braids that define transversal knot types that are not transversally simple. The method of proof is topological and indirect.
Study transverse measures on infinite type hyperbolic surfaces.
By examining knot Floer homology, we extend a result of Ozsváth and Stipsicz and show further infinitely many Legendrian and transversely non-simple knot types among two-bridge knots. We give sufficient conditions of Legendrian and transverse non-simplicity on the continued fraction expansion of the corresponding ratio…
Withdrawn and replaced by two related manuscripts: (1) "Stabilization in the braid groups I:MTWS", published in Geometry and Topology Volume 10 (2006), 413-540, arXiv:math.GT/0310279, and (2) "Stabilization in the braid groups II: Transversal simplicity of knots", Geometry and Topology Volume 10 (2006), to appear, arXi…
A knot type is exchange reducible if an arbitrary closed n-braid representative can be changed to a closed braid of minimum braid index by a finite sequence of braid isotopies, exchange moves and +/- destabilizations. In the manuscript [J Birman and NC Wrinkle, On transversally simple knots, preprint (1999)] a transver…
We study Legendrian knots in a cabled knot type. Specifically, given a topological knot type K, we analyze the Legendrian knots in knot types obtained from K by cabling, in terms of Legendrian knots in the knot type K. As a corollary of this analysis, we show that the (2,3)-cable of the (2,3)-torus knot is not transver…
This paper compares two invariants of foliated manifolds which seem to measure the non-Hausdorffness of the leaf space: the transversal length on the fundamental group and the foliated Gromov norm on the homology. We consider foliations with the property that the set of singular simplices transverse to the foliation sa…
Similar simplices can be inscribed in most smoothly embedded spheres.
The study finds non-simple isotopy classes of links in 3-manifolds, including Legendrian and pseudo-Legendrian examples.
We prove that an isometric action of a Lie group on a Riemannian manifold admits a resolution preserving the transverse geometry if and only if the action is infinitesimally polar. We provide applications concerning topological simplicity of several classes of isometric actions, including polar and variationally comple…
We prove a transversality "lifting property" for compactified configuration spaces as an application of the multijet transversality theorem: the submanifold of configurations of points on an arbitrary submanifold of Euclidean space may be made transverse to any submanifold of the configuration space of points in Euclid…
Study simplicial volume via foliated simplices and duality.
A graph helps understand Artin groups better.
In this expository article, we consider first order elliptic differential operators acting on smooth vector bundles over compact manifolds, and certain invariants derived from the analysis of these operators, namely the eta invariant} and the equivariant index. Many researchers have previously considered these invarian…
The present article proposes a partial answer to the explicit inversion of the tensor tomography problem in two dimensions, by proving injectivity over certain kinds of tensors and providing reconstruction formulas for them. These tensors are symmetric differentials of any order as well as other types obtained after ta…
Let be given a {\em colored 3-pseudo-triangulation} with tetrahedra. Colored means that each tetrahedron have vertices distinctively colored 0,1,2,3. In a {\em pseudo} 3-triangulation the intersection of simplices might be subsets of simplices of smaller dimensions (faces), instead of a single m…
Hedge Funds are considered as one of the portfolio management sectors which shows a fastest growing for the past decade. An optimal Hedge Fund management requires an appropriate risk metrics. The classic CAPM theory and its Ratio Sharpe fail to capture some crucial aspects due to the strong non-Gaussian character of He…
The paper develops formulas for hyperbolic simplices based on edge lengths.
We study the transversal hard Lefschetz theorem on a transversely symplectic foliation. This article extends the results of transversally symplectic flows (H.K.~Pak, "Transversal harmonic theory for transversally symplectic flows", J. Aust. Math. Soc. 84 (2008), 233--245) to the general transversely symplectic foliatio…
Estimates dimensions of maximal simplices for rational and irrational trees in Outer space.
Study on symplectic Dirac operators on foliations, estimating eigenvalues.
The paper establishes conditions for Riemannian connections and semi-simplicity of Lie algebras using spray structures.
It is proved that the volume of spherical or hyperbolic simplices, when considered as a function of the dihedral angles, can be extended continuously to degenerated simplices.
Study on transverse Ricci solitons on compact foliated manifolds.
New examples show transverse knots are determined by their branched covers.
Geodesic simplices in pseudo-hyperbolic space get a cohomological treatment.
Defines transverse symbols for foliated manifolds and proves their K-homology class.
Study transverse Dolbeault cohomology for almost complex structures.
We prove a priori estimates for a class of transverse fully nonlinear equations on Sasakian manifolds and give some geometric applications such as the transversion Calabi-Yau theorem for transverse balanced and (strongly) Gauduchon metrics. We also explain that similar results hold on compact oriented, taut, transverse…
Egorov's theorem for transversally elliptic operators, acting on sections of a vector bundle over a compact foliated manifold, is proved. This theorem relates the quantum evolution of transverse pseudodifferential operators determined by a first order transversally elliptic operator with the (classical) evolution of it…
Study finds non-isotopic transverse tori in Engel manifolds.
New theorem allows transverse links to be braided with rational book structure.
Reidemeister's theorem proved using smooth functions and transversality.
The study classifies transverse spheres in flag manifolds and finds new examples.
We study the transverse Lusternik-Schnirelmann category of a Riemannian foliation on a compact manifold. We obtain a necessary and sufficient condition when the transverse LS category is finite. We also introduce a variation on the concept of transverse LS category, the essential transverse category, and show that this…
We study the transversal wave equation on a compact Riemannian foliated manifold. As applications, we get an Egorov's type theorem for transversally elliptic operators, state a relationship between the singularities of the Fourier transform of the spectrum distribution function of a transversally elliptic operator and …
We study the transversally harmonic maps between foliated Riemannian manifolds. In particular, we prove that under some curvature conditions, any transversally harmonic map is transversally totally geodesic.
Final revision. To appear in the Journal of Differential Geometry. This paper studies knots that are transversal to the standard contact structure in , bringing techniques from topological knot theory to bear on their transversal classification. We say that a transversal knot type $\cTK$ is {\it transversally…
Study on geometry and dynamics of transverse subgroups.
Engel manifolds show transverse tori can be made to have various formal invariants.
We classify positive transversal torus knots in tight contact structures up to transversal isotopy.
Study PL bordism theories with quantitative bounds on filling simplices.
We exhibit pairs of transverse knots with the same self-linking number that are not transversely isotopic, using the recently defined knot Floer homology invariant for transverse knots and some algebraic refinements of it.
A transverse knot is a knot that is transverse to the planes of the standard contact structure on real 3-space. In this paper we prove the Markov Theorem for transverse braids, which states that two transverse closed braids that are isotopic as transverse knots are also isotopic as transverse braids. The methods of the…
We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and produces a three-variable knot polynomial related to the A-polynomial. We provide …
Framework reduces simplicity bias in NNs, improving OOD generalization and robustness.