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 proof of Khovanov homology invariance via Conway mutation.
We define a link homology theory that is readily seen to be both isomorphic to reduced odd Khovanov homology and fully determined by data impervious to Conway mutation. This gives an elementary proof that odd Khovanov homology is mutation invariant, and therefore that mod 2 Khovanov homology is mutation invariant. We a…
Khovanov homology invariant under Conway mutation.
Study shows mutation invariance of arc index for some Montesinos knots.
Genus 2 mutation is the process of cutting a 3-manifold along an embedded closed genus 2 surface, twisting by the hyper-elliptic involution, and gluing back. This paper compares genus 2 mutation with the better-known Conway mutation in the context of knots in the 3-sphere. Despite the fact that any Conway mutation can …
We study the effect of mutation on link concordance and 3-manifolds. We show that the set of links concordant to sublinks of homology boundary links is not closed under positive mutation. We show that mutation does not preserve homology cobordism classes of 3-manifolds. A significant consequence is that there exist 3-m…
The paper studies alternating links in thickened surfaces using flow lattices and disc mutations.
We prove that generalized mutation preserves several geometric invariants such as the volume and Goncharov invariant of Q-rank 1 locally symmetric spaces.
Khovanov-Floer theories are shown to be invariant under mutation.
We prove that Khovanov homology and Lee homology with coefficients in are invariant under component-preserving link mutations.
Study shows Conway mutation preserves a specific link invariant.
Mutation is an operation on 3-manifolds containing an embedded surface of genus 2. It is defined by cutting along the surface and regluing using the `hyperelliptic' involution, and is known to preserve many 3-manifold invariants. I show that mutation of a homology 3-sphere preserves its (instanton) Floer homology, and …
New invariant measures loop iterations in algebraic structures.
We show that instanton knot homology is mutation-invariant, as a consequence of earlier work of the third author.
It is conjectured that the Khovanov homology of a knot is invariant under mutation. In this paper, we review the spanning tree complex for Khovanov homology, and reformulate this conjecture using a matroid obtained from the Tait graph (checkerboard graph) G of a knot diagram K. The spanning trees of G provide a filtrat…
We show that the reduced sl(n) homology defined by Khovanov and Rozansky is invariant under component-preserving positive mutation when n is odd.
Given a hyperbolic knot, we prove that the Reidemeister torsion of any lift of the holonomy to SL(2,C) is invariant under mutation along a Conway sphere.
Zeroth HOMFLY polynomial coefficients can't tell mutant knots apart.
This paper establishes that sutured annular Khovanov homology is not invariant for braid closures under axis-preserving mutations. This follows from an explicit relationship between sutured annular Khovanov homology and the classical Burau representation for braid closures.
In this paper, we prove that the Reidemeister torsion twisted by the adjoint representation, which is considered as a 1-form, on the SU(2)-character variety of a knot exterior is invariant under mutation along a Conway sphere.
We construct a family of hyperbolic link complements by gluing tangles along totally geodesic four-punctured spheres, then investigate the commensurability relation among its members. Those with different volume are incommensurable, distinguished by their scissors congruence classes. Mutation produces arbitrarily large…
The d-invariant of an integral, positive definite lattice L records the minimal norm of a characteristic covector in each equivalence class mod 2L. We prove that the 2-isomorphism type of a connected graph is determined by the d-invariant of its lattice of integral cuts (or flows). As an application, we prove that a re…
New knot invariants derived using quantum cluster algebras.
We show examples of knots with the same polynomial invariants and hyperbolic volumes, with variously coinciding 2-cable polynomials and colored Jones polynomials, which are not mutants.
Several new mutation-periodic quivers of period higher than 1 are introduced as well as the associated discrete dynamical systems. The reduction of these systems is developed using either a presymplectic or a Poisson approach. The presymplectic approach leads to a reduced system whose iteration map is symplectic with r…
Kearton observed that mutation can change the concordance class of a knot. A close examination of his example reveals that it is of 4-genus 1 and has a mutant of 4-genus 0. The first goal of this paper is to construct examples to show that for any pair of nonnegative integers m and n there is a knot of 4-genus m with a…
This paper gives an alternate definition of the Affine Index Polynomial (called the Wriggle Polynomial) using virtual linking numbers and explores applications of this polynomial. In particular, it proves the Cosmetic Crossing Change Conjecture for odd virtual knots and pure virtual knots. It also demonstrates that the…
Defines a local Heegaard Floer theory for tangles.
Modeling correlated mutations in cancer for personalized treatment.
It is known that the first two-variable Links--Gould quantum link invariant is more powerful than the HOMFLYPT and Kauffman polynomials, in that it distinguishes all prime knots (including reflections) of up to 10 crossings. Here we report investigations which greatly expand the set of evaluations o…
New knot polynomials reveal patterns and mutations.
Improved genetic programming by optimizing mutation operators for continuous program search.
We provide a framework for studying the interplay between concordance and positive mutation and identify some of the basic structures relating the two. The fundamental result in understanding knot concordance is the structure theorem proved by Levine: for n>1 there is an isomorphism phi from the concordance group C_n o…
Study links curve singularities to quiver mutations.
Mutation Validation method assesses model fit using mutated training labels without validation sets.
Formula for interior polynomial of bipartite graphs derived from knot theory.
Mathematician summarizes protein geometry and mutation effects.
The paper studies Heegaard Floer homology for manifolds with torus boundaries and proves properties.
Geometric interpretation of tangle invariants using immersed curves.
Paper tackles cancer mutation data challenges by creating useful low-dimensional representations.
Mutation graph of support τ-tilting modules over skew-gentle algebras is connected.
Using computer calculations and working with representatives of pretzel tangles we established general adequacy criteria for different classes of knots and links. Based on adequate graphs obtained from all Kauffman states of an alternating link we defined a new numerical invariant: adequacy number, and computed adequac…
Paper tackles gene mutation prediction for HCC using multi-instance multi-label learning.
Link equivalence determined by Goeritz matrices.
We construct finite volume hyperbolic manifolds with large symmetry groups. The construction makes use of the presentations of finite Coxeter groups provided by Barot and Marsh and involves mutations of quivers and diagrams defined in the theory of cluster algebras. We generalize our construction by assigning to every …
Researchers propose improved multivariate prediction models for HIV drug resistance.
The study explores properties and mutations in oriented matroids, proving new results on Euclidean and non-Euclidean structures.
EDAs with matrix transpose improve Bayesian structure learning performance.