arXiv research

Proves a conjecture for annular links using homology classes.

New measure shows how links can be untangled as twists increase.

In this work we establish the tightest lower bound up-to-date for the minimal crossing number of a satellite knot based on the minimal crossing number of the companion used to build the satellite. If $M$ is the wrapping number of the pattern knot, we essentially show that $c(Sat(P,C))>\frac{M^2}{2}c(C)$. The existence …

The paper studies knots formed by twisting a circle around a base knot and conjectures a linear growth in crossing numbers.

Formulae for Rasmussen invariant of satellite knots with wrapping number 2 proved.

The Morse-Novikov number MN(L) of an oriented link L in the 3-sphere is the minimum number of critical points of a Morse map from the complement of L in the 3-sphere to the circle representing the class of a Seifert surface for L (e.g., the Morse-Novikov number of L is zero if and only if L is fibered). We develop vari…

Multi-output is essential in machine learning that it might suffer from nonconforming residual distributions, i.e., the multi-output residual distributions are not conforming to the expected distribution. In this paper, we propose "Wrapped Loss Function" to wrap the original loss function to alleviate the problem. This…

PAC-Wrap provides provable guarantees for semi-supervised anomaly detection.

Suppose $K$ is a hyperbolic knot in a solid torus $V$ intersecting a meridian disk $D$ twice. We will show that if $K$ is not the Whitehead knot and the frontier of a regular neighborhood of $K \cup D$ is incompressible in the knot exterior, then $K$ admits at most one exceptional surgery, which must be toroidal. Embed…

The study improves genus 1 bridge number bounds for satellite knots.

The paper introduces exponential-wrapped distributions on symmetric spaces for better data modeling.

We introduce a wrapped Gaussian for SPD matrices, enhancing data analysis.

We introduce a vanishing property of adjoint Reidemeister torsions of a cusped hyperbolic 3-manifold derived from the physics of wrapped M5-branes on the manifold. To support our physical observation, we present a rigorous proof for the figure-eight knot complement with respect to all slopes. We also present numerical …

We prove that the wrapped Fukaya category of any $2n$-dimensional Weinstein manifold (or, more generally, Weinstein sector) $W$ is generated by the unstable manifolds of the index $n$ critical points of its Liouville vector field. Our proof is geometric in nature, relying on a surgery formula for Floer cohomology and t…

Proves rigidity of sphere metrics with subsets removed.

Study shows links with unbounded annular Khovanov gradings but bounded Floer gradings.

This is the first of a series of two articles where we construct a version of wrapped Fukaya category $\mathcal W\mathcal F(M\setminus K;H_{g_0})$ of the cotangent bundle $T^*(M \setminus K)$ of the knot complement $M \setminus K$ of a compact 3-manifold $M$, and do some calculation for the case of hyperbolic knots $K …

Latent variable models (LVMs) learn probabilistic models of data manifolds lying in an \emph{ambient} Euclidean space. In a number of applications, a priori known spatial constraints can shrink the ambient space into a considerably smaller manifold. Additionally, in these applications the Euclidean geometry might induc…

Paper establishes an isomorphism between Fukaya category and bordered knot Floer homology.

Worldsheet wraps a 3D mesh sheet onto a single image to synthesize novel views.

We survey aspects of classical combinatorial sutured manifold theory and show how they can be adapted to study exceptional Dehn fillings and 2-handle additions. As a consequence we show that if a hyperbolic knot $β$ in a compact, orientable, hyperbolic 3-manifold $M$ has the property that winding number and wrapping nu…

We study supersymmetric probe M5-branes in the AdS_4 solution that arises from M5-branes wrapped on a hyperbolic 3-manifold M_3. This amounts to introducing internal defects within the framework of the 3d-3d correspondence. The BPS condition for a probe M5-brane extending along all of AdS_4 requires it to wrap a surfac…

Study shows infinite Hofer diameter for Lagrangian orbits in cotangent bundles.

New connection found between shape reconstruction methods and persistent homology.

New method wraps black-box classifiers to reduce bias.

Proves Arnol'd's chord conjecture for conormal bundles.

We define a torus algebra for Heegaard Floer homology.

New solutions of gravity from branes wrapped on orbifolds.

We analyse the geometrical structure of supersymmetric solutions of type II supergravity of the form R^{1,9-n} x M_n with non-trivial NS flux and dilaton. Solutions of this type arise naturally as the near-horizon limits of wrapped NS fivebrane geometries. We concentrate on the case d=7, preserving two or four supersym…

We study the knot invariant called trunk, as defined by Ozawa, and the relation of the trunk of a satellite knot with the trunk of its companion knot. Our first result is ${\rm trunk}(K) \geq n \cdot {\rm trunk}(J)$ where ${\rm trunk}(\cdot)$ denotes the trunk of a knot, $K$ is a satellite knot with companion $J$, and …

Using a hyperKähler rotation on complex structures of a Calabi-Yau 2-fold and rolling of an isotropic 2-submanifold in a symplectic 6-manifold, we construct, by gluing, a natural family of immersed Lagrangian deformations of a branched covering of a special Lagrangian 3-sphere in a Calabi-Yau 3-fold and study how they …

We show that the "geometric models of matter" approach proposed by the first author can be used to construct models of anyon quasiparticles with fractional quantum numbers, using 4-dimensional edge-cone orbifold geometries with orbifold singularities along embedded 2-dimensional surfaces. The anyon states arise through…

Study gauged supergravity, M5-branes, and class R theories, constraining supergravity coefficients and calculating partition functions.

Study volume growth in Milnor fibers using real Lagrangians.

The paper supports a conjecture about a vanishing identity for certain 3-manifolds.

We define a topological quantum membrane theory on a seven dimensional manifold of $G_2$ holonomy. We describe in detail the path integral evaluation for membrane geometries given by circle bundles over Riemann surfaces. We show that when the target space is $CY_3\times S^1$ quantum amplitudes of non-local observables …

Drug-Drug Interactions (DDIs) Extraction refers to the efforts to generate hand-made or automatic tools to extract embedded information from text and literature in the biomedical domain. Because of restrictions in hand-made efforts and their lower speed, Machine-Learning, or Deep-Learning approaches have become more po…

A natural oriented (2k+2)-chain in CP^{2k+1} with boundary twice RP^{2k+1}, its complex shade, is constructed. Via intersection numbers with the shade, a new invariant, the shade number of k-dimensional subvarieties with normal vector fields along their real part, is introduced. For an even-dimensional real variety, th…

New method for knot closures from 1-tangles and annulus twists.

These notes are based on lectures given at the Clay School on Geometry and String Theory, Isaac Newton Institute, Cambridge, 25 March - 19 April 2002. They attempt to provide an elementary and somewhat self contained discussion of the construction of supergravity solutions describing branes wrapping calibrated cycles, …

The study compares on-chain option prices with a model and finds significant differences.

Classifies small links in an unmarked solid torus.

A recent trend observed in traditionally challenging fields such as computer vision and natural language processing has been the significant performance gains shown by deep learning (DL). In many different research fields, DL models have been evolving rapidly and become ubiquitous. Despite researchers' excitement, unfo…

Precision measurements at the LHC often require analyzing high-dimensional event data for subtle kinematic signatures, which is challenging for established analysis methods. Recently, a powerful family of multivariate inference techniques that leverage both matrix element information and machine learning has been devel…

We present a short elementary proof of an existence theorem of certain CAT(-1)-surfaces in open hyperbolic 3-manifolds. The main construction lemma in Calegari and Gabai's proof of Marden's Tameness Conjecture can be replaced by an applicable version of our theorem.

Novel M-theory approach classifies topological phases of matter.

We study the existence of D-brane bound states at threshold in Type II string theories. In a number of situations, we can reduce the question of existence to quadrature, and the study of a particular limit of the propagator for the system of D-branes. This involves a derivation of an index theorem for a family of non-F…

The abstract discusses constructing 3d N=2 gauge theories using surgeries and M5-branes.