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.
Unified Lie structures in homotopy and isotopy calculus.
The Markov Theorem Without Stabilization (MTWS) established the existence of a calculus of braid isotopies that can be used to move between closed braid representatives of a given oriented link type without having to increase the braid index by stabilization. Although the calculus is extensive there are three key isoto…
The Markov Theorem Without Stabilization (MTWS) (see math.GT/0310279) established the existence of a calculus of braid isotopies that can be used to move between closed braid representatives of a given oriented link type without having to increase the braid index by stabilization. Although the calculus is extensive the…
We prove the existence of Lagrangian fillings for -type Legendrian links.
We consider ribbon n-knots for n\geq 2. For such knots we define a set of moves on ribbon disks, and show that any two ribbon disks for isotopic knots are related by a finite sequence of such moves and ambient isotopies. Using this we are able to prove that there is a natural geometric correspondence between ribbon n-k…
The unknot U in S^4 has non-unique smooth spanning 3-balls up to isotopy fixing U. Equivalently there are properly embedded non-separating 3-balls in S^1xB^3 not properly isotopic to 1xB^3. More generally there exist non-separating 3-spheres in S^1xS^3 not isotopic to 1xS^3 and non trivial elements of π_0 Diff_0(S^1xS^…
We construct an isotopy of a planar compactum that is not the restriction of an isotopy of any planar continuum.
A braid-like isotopy for links in 3-space is an isotopy which uses only those Reidemeister moves which occur in isotopies of braids. We define a refined Jones polynomial and its corresponding Khovanov homology which are, in general, only invariant under braid-like isotopies.
New obstructions show some 4-manifold homeomorphisms are pseudo-isotopic but not isotopic.
Approaches 4D Schoenflies via pseudo-isotopy.
We prove that every smoothly embedded surface in a 4--manifold can be isotoped to be in bridge position with respect to a given trisection of the ambient 4--manifold; that is, after isotopy, the surface meets components of the trisection in trivial disks or arcs. Such a decomposition, which we call a \emph{generalized …
Classifies curves up to symplectic isotopy.
Quantum invariants for surfaces in 4D 2-handlebodies.
In this paper we solve the following problem in the affirmative: Let be a continuum in the plane $\complex$ and suppose that $h:Z\times [0,1]\to\complex$ is an isotopy starting at the identity. Can be extended to an isotopy of the plane? We will provide a new characterization of an accessible point in a planar …
Smooth isotopy on cube saves energy with extra dimensions.
A star-like isotopy for oriented links in 3-space is an isotopy which uses only Reidemeister II moves with opposite orientations and Reidemeister III moves with alternating orientations when checking the strands clockwise (or anticlockwise). We define a link polynomial derived from the Jones polynomial which is, in gen…
Refined 1-cocycle for knots helps quantify isotopies.
Classifies isotopy classes of links from Thompson's group F and its subgroup.
Uniform convergence of isotopies implies ambient isotopy, aiding knot equivalence.
Proves a Thom Isotopy Theorem for nonproper semialgebraic maps.
Minimal surfaces and curves can have singularities removed by isotopy.
Improved proofs for topological and smooth pseudo-isotopies of simply connected 4-manifolds.
The study constructs examples of pseudo-isotopic but not isotopic 4-manifold diffeomorphisms.
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.
Veering triangulations link Thurston norm and isotopy of surfaces.
Proof confirms Hamiltonian isotopy of submanifolds.
We construct counterexamples to lifting properties of Hamiltonian and contact isotopies.
This paper introduces two virtual knot theory ``analogues'' of a well-known family of invariants for knots in thickened surfaces: the Grishanov-Vassiliev finite-type invariants of order two. The first, called the three loop isotopy invariant, is an invariant of virtual knots while the second, called the three loop fram…
The symplectic isotopy conjecture states that every smooth symplectic surface in is symplectically isotopic to a complex algebraic curve. Progress began with Gromov's pseudoholomorphic curves [Gro85], and progressed further culminating in Siebert and Tian's proof of the conjecture up to degree 17 [ST05], but fur…
Study embedding calculus and link invariants using functor calculus.
Proof of isotopy invariance in Khovanov link homology.
Classifies smooth isotopy of a specific Lagrangian embedding.
We define an equivalence relation called A-isotopy between finitely determined map-germs, which is a strengthened version of A-equivalence. We consider the number of A-isotopy classes of equidimensional Morin singularities, and some other well-known low-dimensional singularities. We also give an application to stable p…
Study isotopy and concordance for metrics on manifolds with boundary.
This paper investigates dynamics that persist under isotopy in classes of orientation-preserving homeomorphisms of orientable surfaces. The persistence of periodic points with respect to periodic and strong Nielsen equivalence is studied. The existence of a dynamically minimal representative with respect to these relat…
We establish the uniqueness up to Hamiltonian isotopy of the Lagrangian spheres in some four dimensional Stein manifolds.
Constructs pseudo-isotopies with Cerf diagrams and Hatcher-Wagoner invariants for barbell maps.
We present a grid diagram analogue of Carter, Rieger and Saito's smooth movie theorem. Specifically, we give definitions for grid movies, grid movie isotopies and present a definition of grid planar isotopy as a particular subset of the grid diagram moves: stabilization, destabilization and commutation. We show that gr…
Embedding calculus proves convergence for surfaces.
Study geometric characterization of asymptotic pseudodifferential calculus on spinor bundles.
We explain that general differential calculus and Lie theory have a common foundation: Lie Calculus is differential calculus, seen from the point of view of Lie theory, by making use of the groupoid concept as link between them. Higher order theory naturally involves higher algebra (n-fold groupoids).(conceptual, topol…
Secondary Calculus formalizes PDEs using cohomology, simplifying their study.
Paper characterizes isotopies and hyperbolicity of weaves using geodesics.
In arXiv:1207.0332 [cs.LO] was proposed a graphic lambda calculus formalism, which has sectors corresponding to untyped lambda calculus and emergent algebras. Here we explore the sector covering knot diagrams, which are constructed as macros over the graphic lambda calculus.
Extends differential calculus to triole algebras.
Introduces tractors for basic examples and modern differential calculus.
A diagrammatic language for 3D manifolds with boundary.
We examine the N-Koszul calculus for the N-symmetric algebras. The case N=2 corresponds to the Elie Cartan calculus. We conjecture that, as in the case N=2, the N-Cartan calculus extends to manifolds when N>2, which would provide a new type of noncommutative differential geometry.