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 smoothing techniques for topological surfaces in 4-manifolds.
Improved proofs for topological and smooth pseudo-isotopies of simply connected 4-manifolds.
Smooth isotopy on cube saves energy with extra dimensions.
Classifies curves up to symplectic isotopy.
Finite type invariants separate PL links in 3D space.
In this paper we define and study flexible links and flexible isotopy in projective space. Flexible links are meant to capture the topological properties of real algebraic links. We classify all flexible links up to flexible isotopy using Ekholms interpretation of Viros encomplexed writhe.
We prove that a topological contact isotopy uniquely defines a topological contact Hamiltonian. Combined with previous results from [MS11], this generalizes the classical one-to-one correspondence between smooth contact isotopies and their generating smooth contact Hamiltonians and conformal factors to the group of top…
New unknots with geometric constraints exist, proving a long-standing conjecture.
New obstructions show some 4-manifold homeomorphisms are pseudo-isotopic but not isotopic.
Example shows smooth vs topological isotopy in a 4-manifold.
Study on topological pseudo-isotopies of 4-manifolds, proving some cases and finding counterexamples.
New gauge theory invariant detects non-smooth isotopy of -knots.
Various standard texts on differential topology maintain that the level-preserving map defined by the track of an isotopy of embeddings is itself an embedding. This note describes a simple counterexample to this assertion.
Smoothly isotopic surfaces in a 4-manifold are stable isotopic if trivial in the 2-homology.
Introduces a Cost function to measure Legendrian knot obstructions.
Paper defines and analyzes mathematical equivalence of periodic tangles.
This paper studies isotopies of periodic tangles in 3-manifolds using finite covers.
Fractional Dehn twists give a measure of the difference between the relative isotopy class of a homeomorphism of a bordered surface and the Thurston representative of its free isotopy class. We show how to estimate and compute these invariants. We discuss the the relationship of our work to stabilization problems in cl…
We combine Freedman's topology with Eliashberg's holomorphic theory to construct Stein neighborhood systems in complex surfaces, and use these to study various notions of convexity and concavity. Every tame, topologically embedded 2-complex K in a complex surface, after C^0-small topological ambient isotopy, is the int…
The space of n-sided polygons embedded in three-space consists of a smooth manifold in which points correspond to piecewise linear or ``geometric'' knots, while paths correspond to isotopies which preserve the geometric structure of these knots. The topology of these spaces for the case n = 6 and n = 7 is described. In…
Study of Lagrangian submanifolds with Riemannian bounds and their metric properties.
New link found that can't be smoothly deformed.
We discuss the properties of a certain type of Dehn surgery along a Lagrangian torus in a symplectic 4-manifold, known as Luttinger's surgery, and use this construction to provide a purely topological interpretation of a non-isotopy result for symplectic plane curves with cusp and node singularities due to Moishezon.
The paper defines a stratification for Lie groupoids in a tame topology context.
Physical knots and links are one-dimensional submanifolds of R^3 with fixed length and thickness. We show that isotopy classes in this category can differ from those of classical knot and link theory. In particular we exhibit a Gordian Split Link, a two component link that is split in the classical theory but cannot be…
New obstruction found for embedding Riemannian manifolds into Euclidean spaces.
We generalize the "hamiltonian topology" on hamiltonian isotopies to an intrinsic "symplectic topology" on the space of symplectic isotopies. We use it to define the group of strong symplectic homeomorphisms, which generalizes the group of hamiltonian homeomorphisms introduced by Oh and Mull…
We give an overview of various recent results concerning the topology of symplectic 4-manifolds and singular plane curves, using branched covers and isotopy problems as a unifying theme. While this paper does not contain any new results, we hope that it can serve as an introduction to the subject, and will stimulate in…
Solves a problem about deforming symplectic forms on a Klein bottle.
The paper studies elliptic surfaces and proves unique fibered structures.
We define a suitably tame class of singular symplectic curves in 4-manifolds, namely those whose singularities are modeled on complex curve singularities. We study the corresponding symplectic isotopy problem, with a focus on rational curves with irreducible singularities (rational cuspidal curves) in the complex proje…
In this note, we discuss the mean curvature flow of graphs of maps between Riemannian manifolds. Special emphasis will be placed on estimates of the flow as a non-linear parabolic system of differential equations. Several global existence theorems and applications to isotopy problems in geometry and topology will be pr…
Quantum model for knotted graphs from knot theory.
Study of disks in complex projective space with specific fundamental groups.
The paper defines a condition for the finiteness of mapping class groups of Heegaard splittings.
Defines Lorentzian distance on contactomorphisms, proving continuity and finite conditions.
Geometric aspects of the filtration on classical links by k-quasi-isotopy are discussed, including the effect of Whitehead doubling, relations with Smythe's n-splitting and Kobayashi's k-contractibility. One observation is: ω-quasi-isotopy is equivalent to PL isotopy for links in a homotopy 3-sphere (resp. contractible…
For Gamma a finite, connected metric graph, we consider the space of configurations of n points in Gamma with a restraint parameter r dictating the minimum distance allowed between each pair of points. These restricted configuration spaces come up naturally in topological robotics. In this paper, we study the homotopy,…
New method shows nonorientable surfaces in 4D are topologically unknotted.
We prove a neighbourhood theorem for arbitrary knots in contact 3-manifolds. As an application we show that two topologically isotopic Legendrian knots in a contact 3-manifold become Legendrian isotopic after suitable stabilisations.
This is an introductory text on the more topological aspects of contact geometry, written for the Handbook of Differential Geometry vol. 2. After discussing (and proving) some of the fundamental results of contact topology (neighbourhood theorems, isotopy extension theorems, approximation theorems), I move on to a deta…
For a fixed regular cone in Euclidean space with small entropy we show that all smooth self-expanding solutions of the mean curvature flow that are asymptotic to the cone are in the same isotopy class.
Study shows how to create 2-links with any group in 4-manifolds.
New examples show limits of physical link isotopies.
New algebraic structure for 2-string links and long knots.
This paper studies the geometry of the group of all co-Hamiltonian diffeomorphisms of a compact cosymplectic manifold . The fix-point theory for co-Hamiltonian diffeomorphisms is studied, and we use Arnold's conjecture to predict the exact minimum number of fix point that such a diffeomorphism must have (thi…
The paper gives topological as well as rigid isotopy classification of smooth irreducible algebraic curves in the real projective 3-space for the case when the degree of the curve is at most six and its genus is at most one.
Researchers compute Goeritz groups for all (1,1)-link decompositions.