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.
3D transverse links created from complex surfaces and spheres.
Geometric flow on curves in S^3 generates YO equations solutions.
New transverse links solve contact manifold problems.
Study links in contact manifolds using open books and overtwisted disks.
We classify transverse Hopf links in the standard contact 3-space up to transverse isotopy in terms of their components' self-linking number.
New theorem allows transverse links to be braided with rational book structure.
Study transverse and Legendrian invariants of certain link cables using Floer homology.
Study annular concordance invariants and refine transverse link invariants.
Defines an odd analog of Plamenevskaya's invariant for transverse links.
Study proves h-principles for curves in bracket-generating distributions.
Study classifies twist knots with maximal self-linking number in S^3.
Study how braid properties affect transverse link invariants.
We establish some inequalities about the Khovanov-Rozansky cohomologies of braids. These give new upper bounds of the self-linking numbers of transversal links in standard contact which is sharper than the well known bound given by the HOMFLY polynomial. We also introduce a sequence of transversal link invariants…
Stabilization operation for high-dimensional contact manifolds, proving many links are non-simple.
For a word w in the braid group on n-strands, we denote by T_w the corresponding transverse braid in the rotational symmetric tight contact structure on S^3. We exhibit a map on link Floer homology which sends the transverse invariant associated to T_{ws_i} to that associated to T_w, where s_i is one of the standard ge…
We analyze transverse doubled knots in the standard contact 3-space by using spanned clasp disks. As applications, we will estimate their self-linking number and furthermore we will show that in many cases, transverse twist knots with the maximal self-linking number are unique up to transverse isotopy.
We show that a transverse link in a contact structure supported by an open book decomposition can be transversely braided. We also generalize Markov's theorem on when the closures of two braids represent (transversely) isotopic links.
We consider vector fields on knot/link complements in which are transverse to the fibres of a fibration of the complement over a circle. We prove that a large class of fibred knots/links, including all non-torus fibred 2-bridge knots, has the following property: any vector field transverse to the fibres of the fi…
Develops a new spectrum for annular links, recovering a transverse invariant at extreme gradings.
We define an invariant of transverse links in the standard contact 3-sphere as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives a bound on the self-linking number in terms of Rasmussen's invariant s(K). We p…
The paper proves inequalities for links in tight contact 3-manifolds.
We construct a new invariant of transverse links in the standard contact structure on R^3. This invariant is a doubly filtered version of the knot contact homology differential graded algebra (DGA) of the link. Here the knot contact homology of a link in R^3 is the Legendrian contact homology DGA of its conormal lift i…
For any two disjoint oriented circles embedded into the 3-dimensional real projective space, we construct a 3-dimensional configuration space and its map to the projective space such that the linking number of the circles is the half of the degree of the map. Similar interpretations are given for the linking number of …
New method computes transverse knot invariant using braids.
New invariant shows non-zero transverse links in open books.
It is shown that two braids represent transversally isotopic links if and only if one can pass from one braid to another by conjugations in braid groups, positive Markov moves, and their inverses.
Study of cosmetic contact surgeries on knots, excluding some cases.
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.
For any knot T transverse to a given contact structure on a 3-manifold, we exhibit a Legendrian two-component link such that T equals the transverse push-off of one of the link components and contact (+1)-surgery on the link has the same effect as a Lutz twist along T.
Study curves in 3-sphere using invariant geometric flows.
We study a Killing spinor type equation on spin Riemannian flows. We prove integrability conditions and partially classify those Riemannian flows carrying non-trivial solutions to that equation in case is a local Riemannian product, a Sasakian manifold or 3-dimensional.
New inductive basis proves Markov trace existence and transverse traces determination.
Formula for computing rotation and self-linking numbers in contact surgery diagrams.
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…
We review a braid theoretic self-linking number formula and study its applications.
The primary objects of study in the ``knot theory of complex plane curves'' are C-links: links (or knots) cut out of a 3-sphere in the complex plane by complex plane transverse and totally tangential. Transverse C-links are naturally oriented. There are many natural classes of examples: links of singularities; links at…
We prove that a nicely fibered link (by which we mean the binding of an open book) in a tight contact manifold with zero Giroux torsion has a transverse representative realizing the Bennequin bound if and only if the contact structure it supports (since it is also the binding of an open book) is This gives…
Study finds non-isotopic transverse tori in Engel manifolds.
Defines transverse symbols for foliated manifolds and proves their K-homology class.
Classifies Legendrian torus and cable links, revealing symmetries and invariants.
Given a transverse link in the standard contact 3-sphere, we study the contact manifold that arises as a branched double cover of the sphere. We give a contact surgery description of such manifolds, which allows to determine the Heegaard Floer contact invariants for some of them. By example of the knots of Birman--Mena…
Paper defines new invariants from Khovanov homology, linking them to existing ones.
New knot invariant from equivariant Heegaard Floer cohomology.
Algorithm compares Legendrian knots efficiently in some cases.
3D Schoenflies theorem for simply-connected 2-complexes.
New concept of quasi-right-veering for braids helps classify non-loose links.
New technique distinguishes transverse knots, solving equivalence problem.
Polynomial algorithm found for alternating link equivalence.