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 technique distinguishes transverse knots, solving equivalence problem.
We introduce the warping crossing polynomial of an oriented knot diagram by using the warping degrees of crossing points of the diagram. Given a closed transversely intersected plane curve, we consider oriented knot diagrams obtained from the plane curve as states to take the sum of the warping crossing polynomials for…
3D foliations can be approximated by contact structures.
Reeb flow made transverse to foliations without invariant measures.
New proof of Aubin-Yau theorem for complex non-Kähler manifolds.
We characterize the oriented Seifert-fibered three-manifolds which admit positive, transverse contact structures.
The study proves estimates for transverse nonlinear equations on Sasakian manifolds with applications in geometry.
Study shows non-orientable manifolds restrict signature-changing metrics globally.
We show that every co--orientable taut foliation F of an orientable, atoroidal 3-manifold admits a transverse essential lamination. If this transverse lamination is a foliation G, the pair F,G are the unstable and stable foliation respectively of an Anosov flow. Otherwise, F admits a pair of transverse very full genuin…
New Alexander polynomial defined for transverse graphs.
Flow smooths foliations, converging to a transversely Hermitian metric.
We study compatible toric Sasaki metrics with constant scalar curvature on co-oriented compact toric contact manifolds of Reeb type of dimension at least 5. These metrics come in rays of transversal homothety due to the possible rescaling of the Reeb vector fields. We prove that there exist Reeb vector fields for which…
Adapts PDE method to prove estimates for complex Hessian equations.
Study extends geodesic ray transform results to orientable surfaces.
Study affinely transverse foliations in sphere bundles, finding bounds and vanishing conditions.
New theorems on Hodge numbers and Kähler structures derived from complex differential forms.
Characterizes transverse surfaces for pseudo-Anosov flows in 3-manifolds.
We produce the first examples of closed, tight contact 3-manifolds which become overtwisted after performing admissible transverse surgeries. Along the way, we clarify the relationship between admissible transverse surgery and Legendrian surgery. We use this clarification to study a new invariant of transverse knots - …
In this note we give a characterization of taut Riemannian foliations using the transverse divergence. This result turns out to be a convenient tool in the case of some standard examples. Furthermore, we show that a classical tautness result of Haefliger can be obtained in our particular setting as a straightforward co…
Simple flows on manifold foliations.
This paper establishes transversality for perturbed Vafa-Witten moduli spaces on 4-manifolds.
We construct a pair of transverse genuine laminations on an atoroidal 3-manifold admitting transversely orientable uniform 1-cochain. The laminations are induced by the uniform 1-cochain and they are indeed the "straightening" of the coarse laminations defined in [Ca], by using minimal surface techniques. Moreover, whe…
New surfaces in 4-ball differ topologically but not diffeomorphically.
Deformations of the Reeb flow of a Sasakian manifold as transversely Kähler flows may not admit compatible Sasakian metrics anymore. We show that the triviality of the (0,2)-component of the basic Euler class characterizes the existence of compatible Sasakian metrics for given small deformations of the Reeb flow as tra…
We consider the problem of realizing tight contact structures on closed orientable three-manifolds. By applying the theorems of Hofer et al., one may deduce tightness from dynamical properties of (Reeb) flows transverse to the contact structure. We detail how two classical constructions, Dehn surgery and branched cover…
We establish an -principle for exact Lagrangian immersions with transverse self-intersections and the minimal, or near-minimal number of double points. One corollary of our result is that any orientable closed 3-manifold admits an exact Lagrangian immersion into standard symplectic 6-space $\R^6_\st$ with exactly on…
We prove the existence of foliations transverse to pseudo-Anosov flows using veering triangulations.
The paper bounds the -norm of Euler class for foliations on 3-manifolds.
We establish a canonical gluing procedure for Seiberg-Witten monopoles on the two pieces of a closed, oriented 4-manifold X which is split along a 3-dimensional closed, oriented submanifold. We only assume that the (unperturbed) character variety is Kuranishi-smooth and the limiting maps are transversal -- then we will…
Two obstructions found to keep a foliation transverse.
We prove that every closed, smooth -manifold admits a Riemannian metric together with a smooth, transversely oriented CMC foliation if and only if its Euler characteristic is zero, where by CMC foliation we mean a codimension-one, transversely oriented foliation with leaves of constant mean curvature and where t…
It is shown that Legendrian (resp. transverse) cable links in the 3-sphere with its standard tight contact structure, i.e. links consisting of an unknot and a cable of that unknot, are classified by their oriented link type and the classical invariants (Thurston-Bennequin invariant and rotation number in the Legendrian…
Let be a closed, connected, oriented, , Riemannian, n-manifold with a transversely oriented foliation $\boldkey F$. We show that if are basic vector fields, the leaf component of , $\Cal{V}[X,Y]$, has vanishing leaf divergence whenever $κ\wedge χ_{\boldkey F}$ is a c…
Study classifies Einstein 4-manifolds with specific curvature properties.
Expands Euler-Poincare characteristic to supergeometry.
The paper extends Heegaard Floer homology to spatial graphs.
We prove a complete classification theorem for loose Legendrian knots in an oriented 3-manifold, generalizing results of Dymara and Ding-Geiges. Our approach is to classify knots in a -manifold that are transverse to a nowhere-zero vector field up to the corresponding isotopy relation. Such knots are called …
Grid homology properties for MOY graphs studied.
The study examines conditions for Poisson structures on orientable manifolds with specific foliations.
New insights into how neural networks classify data.
Ozsvath and Szabo show that there is a spectral sequence whose E^2 term is the reduced Khovanov homology of L, and which converges to the Heegaard Floer homology of the (orientation reversed) branched double cover of S^3 along L. We prove that the E^k term of this spectral sequence is an invariant of the link L for all…
The paper generalizes a theorem and introduces a new characteristic map for foliated manifolds.
Oriented closed curves on an orientable surface with boundary are described up to continuous deformation by reduced cyclic words in the generators of the fundamental group and their inverses. By self-intersection number one means the minimum number of transversal self-intersection points of representatives of the class…
We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented solenoids with a transversal measure into smooth manifolds, generalizing Ruelle…
New proof of Milnor-Wood inequality for circle bundles.
The Hitchin-Kobayashi correspondence is extended to foliated Riemannian manifolds.
In this paper, we study the global behaviour of contact structures on oriented manifolds V which are circle bundles over a closed orientable surface S of genus g>0. We establish in particular contact analogs of a number of classical results about foliations due to Milnor, Wood, Thurston, Matsumoto, and Ghys. In Section…
Harmonic maps study on surfaces with non-positive curvature.