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.
Paper classifies non-loose knots and discusses conditions for their existence.
A Legendrian or transverse knot in an overtwisted contact 3-manifold is non-loose if its complement is tight and loose if its complement is overtwisted. We define three measures of the extent of non-looseness of a non-loose knot and show they are distinct.
Loose Legendrian knots in rational homology spheres are Legendrian isotopic if they have the same classical invariants.
Classifies knots in a special 3D space.
Study on Legendrian and transverse realizations of negative torus knots.
Classifies Legendrian and transverse torus knots in .
We set forth a definition of hyperfinite knots. Loosely speaking, these are limits of certain sequences of knots with increasing crossing number. These limits exist in appropriate closures of quotient spaces of knots. We give examples of hyperfinite knots. These examples stem from an application of the Thermodynamic Li…
Concrete description of infinite order cork automorphism.
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 …
We show that the presence of a plastikstufe induces a certain degree of flexibility in contact manifolds of dimension 2n+1>3. More precisely, we prove that every Legendrian knot whose complement contains a "nice" plastikstufe can be destabilized (and, as a consequence, is loose). As an application, it follows in certai…
We define invariants of null--homologous Legendrian and transverse knots in contact 3--manifolds. The invariants are determined by elements of the knot Floer homology of the underlying smooth knot. We compute these invariants, and show that they do not vanish for certain non--loose knots in overtwisted 3--spheres. More…
We describe various handle moves in contact surgery diagrams, notably contact analogues of the Kirby moves. As an application of these handle moves, we discuss the respective classifications of long and loose Legendrian knots.
We use monopole Floer homology for sutured manifolds to construct invariants of Legendrian knots in a contact 3-manifold. These invariants assign to a knot K in Y elements of the monopole knot homology KHM(-Y,K), and they strongly resemble the knot Floer homology invariants of Lisca, Ozsváth, Stipsicz, and Szabó. We pr…
Study on transverse knots and their neighborhoods, proving unique standard neighborhoods and destabilization results.
We prove that two Legendrian knots in a contact structure which is trivializable as a plane bundle are Legendrian isotopic provided that (1) they are isotopic as framed knots, (2) they have the same rotation number with respect to some parallelization of the contact structure, and (3) there is an overtwisted disk disjo…
We prove that each overtwisted contact structure has knot types that are represented by infinitely many distinct transverse knots all with the same self-linking number. In some cases, we can even classify all such knots. We also show similar results for Legendrian knots and prove a "folk" result concerning loose transv…
Loosely speaking, the Volume Conjecture states that the limit of the n-th colored Jones polynomial of a hyperbolic knot, evaluated at the primitive complex n-th root of unity is a sequence of complex numbers that grows exponentially. Moreover, the exponential growth rate is proportional to the hyperbolic volume of the …
Research on knots, braids, and their invariants.
In this note, we define a new invariant of a Legendrian knot in a contact manifold using an open book decomposition supporting the contact structure. We define the support genus sg(L) of a Legendrian knot L in a contact 3-manifold (M, ξ) as the minimal genus of a page of an open book of M supporting the contact structu…
New twist classes help classify contact structures and looseness.
This is a survey on contact open books and contact Dehn surgery. The relation between these two concepts is discussed, and various applications are sketched, e.g. the monodromy of Stein fillable contact 3-manifolds, the Giroux-Goodman proof of Harer's conjecture on fibred links, construction of symplectic caps to filli…
Proves h-principle for loose Legendrian embeddings in contact topology.
New property ensures non-looseness of ribbon boundaries.
Research shows that certain metric spaces cannot contain rigid structures and provides evidence for loose embeddings into Euclidean spaces.
Quantum isometry groups extend to all countable metric spaces, and loose embeddings help understand metric space relationships.
Disproves the Smale Conjecture for S^4 by showing Diff(S^4) is not SO(5).
Classifies Legendrian Hopf links in lens spaces.
Homotopy 4-spheres created by iterated Gluck twists of S^4.
Standard proved to be diffeomorphic to a curious homotopy sphere.
A new quantum relation connects exceptional Lie algebras and knots.
We construct an infinite order loose cork.
The article classifies Engel structures up to homotopy.
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 …
Loose bounds found for least-norm interpolant in over-parameterized settings.
New algorithm learns coordinated decisions in loosely-coupled multi-agent systems.
We consider the structure learning problem for graphical models that we call loosely connected Markov random fields, in which the number of short paths between any pair of nodes is small, and present a new conditional independence test based algorithm for learning the underlying graph structure. The novel maximization …
Classifies Legendrian unknots in overtwisted contact structures.
This paper centers around two basic problems of topological coincidence theory. First, try to measure (with help of Nielsen and minimum numbers) how far a given pair of maps is from being loose, i.e. from being homotopic to a pair of coincidence free maps. Secondly, describe the set of loose pairs of homotopy classes. …
LC-FL uses generative models to reduce communication costs in federated learning.
The (constrained) minimization of a ratio of set functions is a problem frequently occurring in clustering and community detection. As these optimization problems are typically NP-hard, one uses convex or spectral relaxations in practice. While these relaxations can be solved globally optimally, they are often too loos…
Study of contractible manifolds and their twists to determine if they are .
Given two maps f1 and f2 from the sphere Sm to an n-manifold N, when are they loose, i.e. when can they be deformed away from one another? We study the geometry of their (generic) coincidence locus and its Nielsen decomposition. On the one hand the resulting bordism class of coincidence data and the corresponding Niels…
In this note we announce results on the mean curvature flow of mean convex sets in 3-dimensions. Loosely speaking, our results justify the naive picture of mean curvature flow where the only singularities are neck pinches, and components which collapse to asymptotically round spheres.
The study explores Legendrian invariants and half Giroux torsion in contact structures.
InfoNCE objective is equivalent to ELBO in RPM, linking to self-supervised learning.
Paper tightens optimization bounds using conformal prediction.
Gossip-based actor-learner architectures improve deep reinforcement learning efficiency and scalability.
Study fractional twist behavior in branched covers, with applications to 3-manifolds.