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.
Computes Kauffman bracket polynomial for specific 2-tangle shadows.
Growth functions of Coxeter groups and the Poincare series of Kleinian and Fuchsian singularities are -tangle -fractions.
Study tangle equations linking enzyme actions to knot theory.
We construct the universal sl(2)-tangle cohomology using an approach with webs and dotted foams. This theory depends on two parameters, and for the case of links it is a categorification of the unnormalized Jones polynomial of the link.
The paper introduces a cobordism for Khovanov homology crossing change and categorifies Vassiliev skein relations.
In this paper, We introduce an invariant of rational n-tangles which is obtained from the Kauffman bracket. It forms a vector with Laurent polynomial entries. We prove that the invariant classifies the rational 2-tangles and the reduced alternating rational 3-tangles. We conjecture that it classifies the rational 3-tan…
We note that a rational -tangle diagram is obtained from a combination of four generators. There is an algorithm to distinguish two rational -tangle diagrams up to isotopy. However, there is no perfect classification about rational -tangle diagrams such as the classification of rational -tangle diagrams cor…
We define an elementary relatively graded Lagrangian-Floer chain complex for restricted immersions of compact 1-manifolds into the pillowcase, and apply it to the intersection diagram obtained by taking traceless character varieties of 2-tangle decompositions of knots. Calculations for torus knots…
We construct a bigraded (co)homology theory which depends on a parameter a, and whose graded Euler characteristic is the quantum sl(2) link invariant. We follow Bar-Natan's approach to tangles on one side, and Khovanov's sl(3) theory for foams on the other side. Our theory is properly functorial under tangle cobordisms…
Mutant knots, in the sense of Conway, are known to share the same Homfly polynomial. Their 2-string satellites also share the same Homfly polynomial, but in general their m-string satellites can have different Homfly polynomials for m>2. We show that, under conditions of extra symmetry on the constituent 2-tangles, the…
Given a compact oriented 3-manifold M in S^3 with boundary, an (M,2n)-tangle T is a 1-manifold with 2n boundary components properly embedded in M. We say that T embeds in a link L in S^3 if T can be completed to L by a 1-manifold with 2n boundary components exterior to M. The link L is called a closure of T. We define …